on l1 invariant sequence spaces abstract we introduce and investigate a new sectional property for topological sequence spaces which we call the kb property it turns out that multipliers into l and multiplication by l 1 play a very similar role for kb as multipliers into bs and multiplication by bv 0 do for the well known sectional property ab however we also encounter significant differences one of these differences motivates the study of l 1 invariant sequence spaces that is sequence spaces e with l 1 e e

on weighted statistical convergence based on p q integers and related approximation theorems for functions of two variables abstract in this work we first define a difference operator p q m of natural order m with respect to p q integers we then introduce the concepts of p q m statistical convergence statistical p q m summability and strong p q m summability of order by the weighted method furthermore based on the definition of statistical p q m summability we prove a korovkin type approximation theorem for functions of two variables by using p q analogue of bernstein operator of two variables we give an example which shows that proposed method successfully works finally some voronovskaja type approximation results are obtained

the relationship between the jacobi and the successive overrelaxation sor matrices of a k cyclic matrix abstract let a be a k l l generalized consistently ordered matrix with t and l its associated jacobi and sor matrices whose eigenvalues and satisfy the well known relationship 1 k k k k 1 for a subclass of the above matrices a we prove that the matrix analogue of the previous relationship holds exploiting the matrix relationship we show that the sor method is equivalent to a certain monoparametric k step iterative one when used for the solution of the fixed point problem x tx c

on the fine spectra of the generalized rth difference operator δνr on the sequence space l1 abstract the main purpose of this paper is to determine the spectrum and the fine spectrum of the r th difference operator r on sequence space l 1 the operator r over l 1 is defined by r x r x k k 0 r 1 x k r 1 x k 1 k 0 with x k k 0 for k 0 where x x k l 1 r n and k is either constant or strictly decreasing sequence of positive real numbers satisfying certain conditions

matrix transformations between the sequence spaces of maddox abstract the sequence spaces of maddox l p c 0 p c p and l p with a sequence p p k as parameter generalise the classical sequence spaces l 1 c 0 c and l in this paper toeplitz conditions are derived for matrices to map a maddox sequence space into another such space

a survey of the iterative methods for the solution of linear systems by extrapolation relaxation and other techniques abstract for the iterative solution of linear systems of algebraic equations ax b 1 with a c n n x b c n and det a 0 numerous methods exist although a classification of them seems not to be possible one may note that the first step for the construction of an iterative method usually begins with a splitting of a in 1 thus a is written as a m n where det m 0 and m is easily inverted so that 1 is equivalent to x tx c 2 t m 1n c m 1 the discussion will be restricted to the so called linear stationary iterative methods although some nonstationary ones will be mentioned and emphasis will be given to those which fall into the categories of extrapolation relaxation and similar ones for this it will be assumed that the spectrum t of t in 2 is contained in a well defined compact region r whose complement with respect to the complex plane is simply connected and 1 r under these assumptions and for each specific class of methods described each time an attempt will be made to present the optimum one the optimum is the one out of the class of methods for which the sequence of vectors yielded converges asymptotically to the unique solution of 1 as fast as possible

improved approximation and error estimations by king type p q szasz mirakjan kantorovich operators abstract in the present paper two different modifications are proposed for p q szasz mirakjan kantorovich operators which preserve some test functions some approximation results with the help of better known korovkin s theorem and weighted korovkin s theorem for these operators are presented furthermore convergence properties in terms of modulus of continuity and class of lipschitz functions are studied it has been shown that for a given absolute error bound king type modified p q szasz mirakjan kantorovich operators require lesser value of m and elapsed time within some subintervals further for comparisons some graphics and error estimation tables are presented using matlab r2018a

on the fine spectrum of the difference operator δ on c 0 and c in the present paper the fine spectrum of the difference operator on the sequence spaces c0 and c have been examined and a mercerian theorem has also been given

some new sequence spaces derived by the domain of generalized difference matrix let l denote any one of the classical spaces c c 0 and p of bounded convergent null and absolutely p summable sequences respectively and l also be the domain of the generalized difference matrix b r s in the sequence space l where 1 p the present paper is devoted to studying on the sequence space l furthermore the b and c duals of the space l are determined and the schauder bases for the spaces c c 0 and p are given and some topological properties of the spaces c 0 1 and p are examined finally the classes l 1 l 2 and l 1 l 2 of infinite matrices are characterized where l 1 c c 0 p 1 and l 2 c c 0 1

renormalization group and analyticity in one dimension a proof of dobrushin s theorem we consider one dimensional systems described by many body potentials with finite first moment and prove that the correlation functions are analytic in the interaction parameters this result is not new dobrushin 1973 but our proof is simpler and physically more transparent we show that by introducing suitable blocks and averaging over the variables associated to a subset of the blocks decimation procedure the resulting effective interaction is such that the system can always be dealt with as a high temperature system

chaos butterflies also generate phase transitions we exhibit examples of mixing subshifts of finite type and of continuous potentials such that there are phase transitions but the pressure is always strictly convex more surprisingly we show that the pressure can be analytic on some interval although there exist several equilibrium states

on compact operators and some euler b m difference sequence spaces abstract altay and basar 2005 1 and altay basar and mursaleen 2006 2 introduced the euler sequence spaces e 0 t e c t and e t basarir and kayikci 2009 3 defined the b m difference matrix and studied some topological and geometric properties of some generalized riesz b m difference sequence space in this paper we introduce the euler b m difference sequence spaces e 0 t b m e c t b m and e t b m consisting of all sequences whose b m transforms are in the euler spaces e 0 t e c t and e t respectively moreover we determine the and duals of these spaces and construct the schauder basis of the spaces e 0 t b m and e c t b m finally we characterize some matrix classes concerning the spaces e 0 t b m and e c t b m and give the characterization of some classes of compact operators on the sequence spaces e 0 t b m and e t b m

some approximation results by p q analogue of bernstein stancu operators in this paper we introduce a new analogue of bernstein stancu operators based on p q integers which we call as p q bernstein stancu operators we study approximation properties for these operators based on korovkin s type approximation theorem and also study some direct theorems furthermore we give comparisons and some illustrative graphics for the convergence of operators to some function

generalization of the sequence space l p derived by weighted mean abstract the sequence space l p was introduced and studied by maddox i j maddox spaces of strongly summable sequences quart j math oxford 2 18 1967 345 355 in the present paper the sequence spaces l u v p of non absolute type which is derived by the generalized weighted mean is defined and proved that the spaces l u v p and l p are linearly isomorphic besides this the and duals of the space l u v p are computed and the basis of that space is constructed further it is established that the sequence space l p u v has ad property and given f dual of the space l p u v finally the matrix mappings from the sequence spaces l u v p to the sequence space and from the sequence space to the sequence space l u v p are characterized

some new difference sequence spaces of fractional order and their dual spaces the main objective of the present paper is to introduce certain difference sequence spaces of fractional order and investigate their topological structures as well as some interesting results concerning the fractional difference operator d a in this paper we define some new difference sequence spaces such as c d a u c 0 c d a u and c c d a u by introducing a fractional difference operator d a and for a positive fraction a the difference operator d a is defined by d a x k i 0 1 i c a 1 i c a i 1 x k i also we establish their a b and c duals

on the fine spectrum of the operator b r s t over the sequence spaces l p and bvp 1 p the main purpose of this paper is to determine the fine spectrum with respect to the goldberg s classification of the operator b r s t defined by a triple band matrix over the sequence spaces p and bv p with 1

some new paranormed difference sequence spaces and weighted core in this study we define new paranormed sequence spaces by combining a generalized weighted mean and a difference operator furthermore we compute the a b email protected duals and obtain bases for these sequence spaces besides this we characterize the matrix transformations from the new paranormed sequence spaces to the spaces c 0 q c q q and q finally weighted core of a complex valued sequence has been introduced and we prove some inclusion theorems related to this new type of core

certain topological properties and duals of the domain of a triangle matrix in a sequence space the matrix domain of the particular limitation methods cesaro riesz difference summation and euler were studied by several authors in the present paper certain topological properties and and duals of the domain of a triangle matrix in a sequence space have been examined as an application of the characterization of the related matrix classes

optimal p cyclic sor for complex spectra abstract we consider the successive overrelaxation sor method for the solution of a linear system ax b when the matrix a has a block p p partitioned p cyclic form and its associated block jacobi matrix jp is weakly cyclic of index p following the pioneering work by young and varga in the 1950s many researchers have considered various cases for the spectrum jp and have determined optimal values for the relaxation factor 0 2 so that the sor method converges as fast as possible after the most recent work on the best block p cyclic repartitioning and that on the solution of large scale systems arising in queueing network problems in markov analysis the optimization of the convergence of the p cyclic sor for more complex spectra jp has become more demanding here we state the one point problem for the general p cyclic complex sor case the existence and the uniqueness of its solution are established by analyzing and developing further the theory of the associated hypocycloidal curves for the determination of the optimal parameter s an algorithm is presented and a number of illustrative numerical examples are given

weighted statistical convergence and its application to korovkin type approximation theorem abstract the concept of weighted statistical convergence was introduced and studied by karakaya and chishti 2009 7 in this paper we modify the definition of weighted statistical convergence and find its relationship with the concept of statistical summability n p n due to moricz and orhan 2004 10 we apply this new summability method to prove a korovkin type approximation theorem by using the test functions 1 e x e 2 x we apply the classical baskakov operator to construct an example in support of our result

on the b difference sequence space derived by generalized weighted mean and compact operators abstract in the present paper by using generalized weighted mean and difference matrix b we introduce the paranormed sequence space l u v p b which consist of all sequences whose generalized weighted b difference means are in the linear space l p introduced by i j maddox also we give the basis of this space and compute its and duals further we characterize the classes of matrix mappings from l u v p b to l c and c 0 finally we apply the hausdorff measure of noncompactness to characterize some classes of compact operators given by matrices on the space l p u v b 1 p

some new paranormed sequence spaces maddox defined the sequence spaces l p c p and c0 p in proc camb philos soc 64 1968 335 quart j math oxford 2 18 1967 345 in the present paper the sequence spaces a0r u p and acr u p of non absolute type have been introduced and proved that the spaces a0r u p and a0r u p are linearly isomorphic to the spaces c0 p and c p respectively besides this the and duals of the spaces a0r u p and acr u p have been computed and their basis have been constructed finally a basic theorem has been given and later some matrix mappings from a0r u p to the some sequence spaces of maddox and to some new sequence spaces have been characterized

on the euler sequence spaces which include the spaces lp and l ii abstract by e p r we mean the space of all sequences whose euler transforms of order r are in the sequence spaces l p and l see b altay f basar m mursaleen on the euler sequence spaces which include the spaces l p and l i inform sci 2005 in press where 1 p in the present paper we essentially characterize the classes e p r l e 1 r l p and e p r f of infinite matrices for 1 p and give the characterizations of some other matrix mappings from the space e p r to the euler riesz difference etc sequence spaces by means of a given basic lemma we devote the final section of the paper to examining some geometric properties of the space e p r

modularly weighted four dimensional matrix summability with application to korovkin type approximation theorem abstract this work is concerned with various weighted four dimensional matrix summability methods in modular function spaces associating with generalized difference operator involving p q gamma function following very recent results of kadak 2017 20 we first introduce a new type of difference operator on double function sequences and also define modularly weighted a statistical convergence and modularly statistically n a summability by means of weighted four dimensional regular matrix a we also present some important inclusion relations between newly proposed summability methods moreover based on the concept of modularly statistically n a summability we prove a korovkin type approximation theorem for functions of two variables in modular spaces finally in order to show that our proposed method and its applications to approximation results are stronger than the existing methods we display an illustrative example using bivariate p q bernstein kantorovich operators

weighted statistical convergence based on generalized difference operator involving p q gamma function and its applications to approximation theorems abstract in this work following a new approach of baliarsingh 2016 6 we introduce the concepts of statistically weighted p q summability weighted p q statistical convergence and weighted strongly p q summability with respect to the difference operator h p q including p q analogue of gamma function some inclusion relations between newly proposed methods are examined we then prove a korovkin type approximation theorem for functions of two variables and also present an example via p q analogue of modified bernstein schurer operators to show that our proposed method is stronger than its classical and weighted statistical versions furthermore we compute the rate of convergence of approximating positive linear operators through the modulus of continuity finally we present computational and geometrical approaches to illustrate some of our results in this paper

some recent results on the modified sor theory abstract for the solution of the linear system ax i t x c 1 where t is a weakly cyclic of index p 2 matrix of a special structure the block sor method with different relaxation factors associated with the row blocks of a is considered first a well known relationship connecting the eigenvalue spectra of the block jacobi matrix t of a and its associated modified sor msor matrix is proved for all p 3 via an approach due to varga niethammer and cai next it is shown that the matrix analogue of the eigenvalue relationship holds at least for p 3 this together with the facts that the matrix analogue holds true for p 2 and also for any p 3 provided all relaxation factors coincide suggests a more general validity of the aforementioned matrix identity then based on the matrix relationship an equivalence is established between the msor method and a stationary p parameter p step iterative one for the solution of 1 so one can study convergence properties and determine optimal parameters of both methods by studying the simpler of the two that is the p step one finally some applications of the theory developed when p 2 are presented and a brief discussion concerning comparisons of the optimum msor and aor methods in a specific case is given

generalized weighted statistical convergence and application the object of this paper is to introduce the concepts of weighted l statistical convergence and statistical summability n l p we also establish some inclusion relations and some related results for these new summability methods further we determine a korovkin type approximation theorem through statistical summability n l p and we show that our approximation theorem is stronger than classical korovkin theorem by using classical bernstein polynomials

an adaptive method for solving nonsymmetric linear systems involving applications of scpack consider the following large system of linear equations rm x it t x bf c eqno 0 where it is assumed that t is n by n real matrix with 1 excluded from the spectrum of t and that c is a real vector of dimension n this dissertation uses the results from function theory approximation theory and conformal mapping theory and constructs an adaptive numerical method to solve equation 0 with the aid of scpack this adaptive method periodically estimates the eigenvalue set to obtain near asymptotically optimal rates of convergence of the associated k l step semiiterative methods

on some new generalized sequence spaces abstract in this paper we define the sequence sets l u 2 p c u 2 p and c0 u 2 p and give and duals of these sets further we investigate matrix transformations in the spaces and give a characterization of the class l u 2 p l

iterative and semi iterative methods for computing stationary probability vectors of markov operators iterative and semi iterative methods for computing stationary prob ability vectors of markov type operators are proposed and their convergence properties are analyzed the methods studied apply to certain classes of prob lems in infinite dimensional spaces as well as to classical n x n stochastic ma trices

almost convergence and generalized difference matrix let f denotes the space of almost convergent sequences introduced by lorentz g g lorentz a contribution to the theory of divergent sequences acta math 80 1948 167 190 and f also be the domain of the generalized difference matrix b r s in the sequence space f in this paper the b and c duals of the spaces f fs and f are determined furthermore two basic results on the space f are proved and the classes f m and m f of infinite matrices are characterized and the characterizations of some other classes are also given as an application of those main results where m is any given sequence space

matrix transformations between sequence spaces of generalized weighted means the main object of this paper is to introduce and study some sequence spaces which arise from concept of weighted means determine their b duals and characterize matrix transformations between them

on the fine spectrum of the operator δa b over the sequence space c in this paper we examine the fine spectrum of the generalized difference operator d a b over the sequence space c the boundedness of the operator d a b has been proved also the norm of this operator has been found the class of the operator d a b includes some other special cases such as the generalized difference operator b r s introduced by altay and basar in 2005 our results not only generalize the corresponding results in the existing literature but also give results for some more operators

some new difference sequence spaces the difference sequence spaces d c d and c 0 d were studied by kizmaz canad math bull 24 2 1981 169 the sequence spaces a 0 r and a c r have been recently defined and examined by aydin and basar in hokkaido math j in press the main purpose of the present paper is to introduce the spaces a r 0 d and a r c d of difference sequences moreover it is proved that the spaces a r 0 d and a r c d are the bk spaces including the spaces c 0 and c and some inclusion relations have been given it is also proved that the sequence space a 0 r has ad property while the space a 0 r d has not furthermore the basis and the a b and c duals of the spaces a r 0 d and a r c d have been determined the last section of the paper has been devoted to theorems on the characterizations of the matrix classes a r c d p and a r c d c and the characterizations of some other matrix classes have been obtained by means of a given basic lemma where 1

the analysis ofk step iterative methods for linear systems from summability theory using the theory of euler methods from summability theory we investigate general iterative methods for solving linear systems of equations in particular for a given euler method a regions of the complex plane is determined such that ak step iterative method converges if the eigenvalues of an iteration operatort are contained ins for a givens optimal methods are described and upper and lower bounds are derived for the associated asymptotic rate of convergence special attention is given to two step methods with complex parameters

the fixed point property in banach spaces with the nus property abstract in this paper we show that the weak nearly uniform smooth banach spaces have the fixed point property for nonexpansive mappings

a note on compact operators on matrix domains abstract we establish some identities or estimates for the operator norms and hausdorff measures of noncompactness of linear operators given by infinite matrices that map the matrix domains of triangles in arbitrary bk spaces with ak or in the spaces of all convergent or bounded sequences into the spaces of all null convergent or bounded sequences or of all absolutely convergent series furthermore we apply these results to the characterizations of compact operators on the matrix domains of triangles in the classical sequence spaces and on the sequence spaces studied in i djolovic compact operators on the spaces a 0 r and a c r j math anal appl 318 2 2006 658 666 i djolovic on the space of bounded euler difference sequences and some classes of compact operators appl math comput 182 2 2006 1803 1811

polynomials by conformal mapping for the richardson iteration method for complex linear systems some methods using conformal mappings for determining polynomials for the richardson iteration scheme for complex linear systems a bf x bf b are described the polynomials can be computed fairly rapidly and give rise to iterative schemes with a rate of convergence very close to optimal the methods described are applicable when the eigenvalues of the matrix a lie in a known bounded simply connected region omega in the complex plane omega is assumed to have a smooth boundary

richardson s iteration for nonsymmetric matrices abstract to solve the linear n n system 1 ax a for any nonsingular matrix a richardson s iteration 2 x j 1 x j j ax j a j 1 2 n which is applied in a cyclic manner with cycle length n is investigated where the j are free parameters the objective is to minimize the error x n 1 x where x is the solution of 1 if the spectrum of a is known to lie in a compact set s one is led to the chebyshev type approximation problem 3 min p 1 v n max z s p z where v n is the linear span of z z 2 z n if p solves 3 then the reciprocals of the zeros of p are optimal iteration parameters j it is shown that for a real problem 1 the iteration 2 can be carried out with real arithmetic alone even when there are complex j the stationary case n 1 is solved completely i e for all compact sets s the problem 3 is solved explicitly as a consequence the converging stationary iteration processes can be characterized for arbitrary closed disks s the problem 3 can be solved for all n n and a simple proof is provided the lemniscates associated with s are introduced they appear as an important tool for studying the stability of the iteration 2

generalized difference sequence spaces and their dual spaces the definition of the p p and p duals of a sequence space was defined by et internat j math math sci 24 2000 785 791 in this paper we compute p and n duals of the sequence spaces mv x for x l c and c0 and compute and duals of the sequence spaces mv x for x l c and c0

on p q analogue of bernstein operators in this paper we introduce a new analogue of bernstein operators and we call it as p q bernstein operators which is a generalization of q bernstein operators we also study approximation properties based on korovkin s type approximation theorem of p q bernstein operators and establish some direct theorems furthermore we show comparisons and some illustrative graphics for the convergence of operators to a function

optimal stretched parameters for the sor iterative method noutsos d optimal stretched parameters for the sor iterative method journal of computational and applied mathematics 48 1993 293 308 linear systems whose associated block jacobi matrices j are p cyclic consistently ordered are considered in a number of papers the case of r j p c cyj pp where y p are real nonnegative numbers with 3 1 is studied by using cusped hypocycloids and also by using shortened hypocycloids in this paper the sor method is studied by using stretched hypocycloids the optimal stretched parameters and the corresponding optimal spectral radii are found and their behaviour is studied finally a comparison with the corresponding shortened and cusped sor parameters and spectral radii is also made

on the euler sequence spaces which include the spaces l p and l i in the present paper we introduce the euler sequence space e p r consisting of all sequences whose euler transforms of order r are in the space p of non absolute type which is the bk space including the space p and prove that the spaces e p r and p are linearly isomorphic for 1

on an ssor matrix relationship and its consequences a matrix relationship connecting the jacobi and the symmetric successive overrelaxation ssor matrices associated with a k cyclic consistently ordered matrix a is presented next the equivalence of the ssor method and a certain monoparametric k step one for the solution of the linear algebraic system ax b is established the aforementioned equivalence can be exploited to derive regions of convergence optimum parameters involved etc of the two iterative methods above this is done by studying the simplest of the two methods that is the monoparametric k step one to show how the idea works the case k 2 is very briefly discussed

generalized spaces of difference sequences abstract let l c and c 0 be the banach spaces of bounded convergent and null sequences x x k 1 respectively write x x k x k 1 1 and 2 x x k x k 1 1 in canad math bull 24 1981 169 176 h kizmaz has introduced and studied the sequence spaces e x x e where e c 0 c l recently doga mat 17 1993 18 24 mikail et defined the sets e 2 x 2 x e he obtained duals of these sets and characterized the matrix class e f 2 where e f c 0 c l in this paper we generalize these sets and define e u 2 x u 2 x e where u u k is another sequence such that u k 0 k 1 2 we obtain and duals of these sets and further we characterize the matrix classes e u 2 f and e f u 2

fine spectrum of the generalized difference operator δuv on sequence space l1 abstract in this paper we obtained spectrum and point spectrum of the operator uv on l1 the operator uv on l1 is defined as uv x u n x n v n 1 x n 1 n 0 under certain conditions where x 1 0 and x xn l1 further the results on continuous spectrum residual spectrum and fine spectrum of the operator uv on the sequence space l1 are also derived

convergence of a direct iterative method for large scale least squares problems abstract in 1975 chen and gentleman suggested a 3 block sor method for solving least squares problems based on a partitioning scheme for the observation matrix a into a a 1 a 2 where a1 is square and nonsingular in many cases a1 is obvious from the nature of the problem this combined direct iterative method was discussed further and applied to angle adjustment problems in geodesy where a1 is easily formed and is large and sparse by plemmons in 1979 recently niethammer de pillis and varga have rekindled interest in this method by correcting and extending the sor convergence interval the purpose of our paper is to discuss an alternative formulation of the problem leading to a 2 block sor method for this formulation it is shown that the resulting direct iterative method always converges for sufficiently small sor parameter in contrast to the 3 block formulation formulas for the optimum sor parameter and the resulting asymptotic convergence factor based upon a2a 11 2 are given furthermore it is shown that this 2 cyclic block sor method always gives better convergence results than the 3 cyclic one for the same amount of work per iteration the direct part of the algorithm requires only a sparse matrix factorization of a1 our purpose here is to establish theoretical convergence results in line with the purpose of the recent paper by niethammer de pillis and varga practical considerations of choosing a1 in certain applications and of estimating the resulting a2a 11 2 will be addressed elsewhere

on the fine spectrum of the generalized difference operator b r s over the sequence spaces lp and bvp 1 p abstract the main purpose of this paper is to determine the fine spectrum of the operator b r s defined by a band matrix over the sequence spaces l p and b v p with 1 p since the operator b r s is reduced to the right shift difference and zweier matrices in the special cases r s 0 1 r s 1 1 and r s r 1 r respectively our results are more general than the corresponding results in the existing literature

statistical weighted b summability and its applications to approximation theorems in this paper which deals essentially with various summability concepts and summability techniques and shows how these concepts and techniques lead to a number of approximation results we have used the new concept of weighted a summability proposed by mohiuddine 2016 and introduced the notions of statistically weighted b summability and weighted b statistical convergence with respect to the weighted regular method we then prove a korovkin type approximation theorem for functions of two variables and also present an example via generalized meyer konig and zeller type operator to show that our proposed method is stronger than its classical and statistical versions furthermore the rate of convergence of approximating positive linear operators are estimated by means of the modulus of continuity and some voronovskaja type results are investigated computational and geometrical approaches to illustrate some of our results are also presented

a parallelizable sor like method systems with plus shaped and linear spectra abstract the classical sor method replaces an invertible cyclic linear system in b x f with a family of systems i n b x f where for some optimal scalar b the spectrum of b b is circular the eigenvalues of b are linearly placed falling on the real line moreover the spectral radius of b b is less than that of b similarly this paper explores a tensor mechanism which converts more general systems in b x f to equivalent systems i 2n b x f where the spectrum of b may be plus shaped the spectrum of b is circular and x col 0 x as in the sor theory the spectral radius of b is less than that of b among other things we recapture the results of the sor theory improve on some known results and extend our theory directly to matrices in b which need not be symmetric yet have real plus and minus valued eigenvalues

λ2 weighted statistical convergence and korovkin and voronovskaya type theorems in this paper we propose to introduce a new 2 weighted statistical convergence based upon this definition we prove some korovkin type theorems we also find the rate of the convergence for this kind of weighted statistical convergence and derive some voronovskaya type theorems

gbs operators of bernstein schurer kantorovich type based on q integers agrawal et al 2015 constructed a bivariate generalization of a new kind of kantorovich type q bernstein schurer operators and studied a voronovskaja type theorem and the rate of convergence in terms of the lipschitz class function and the complete modulus of continuity the concern of this paper is to obtain the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and the peetre s k functional finally we construct the gbs generalized boolean sum operators of bivariate q bernstein schurer kantorovich type and estimate the rate of convergence for these operators with the help of mixed modulus of smoothness

a study of semiiterative methods for nonsymmetric systems of linear equations given a nonsingular linear systema x b a splittinga m n leads to the one step iteration 1 x m t x m 1 c witht m 1n andc m 1 b we investigate semiiterative methods sim s with respect to 1 under the assumption that the eigenvalues oft are contained in some compact set of with 1 there exist sim s which are optimal with respect to but except for some special sets such optimal methods are not explicitly known in general using results about maximal convergence of polynomials and uniformly distributed nodes from approximation and function theory we describe here sim s which are asymptotically optimal with respect to it is shown that euler methods extensively studied by niethammer varga nv are special sim s various algorithms for sim s are also derived here a 1 1 correspondence between euler methods and sim s generated by generalized faber polynomials is further established here this correspondence gives that asymptotically optimal euler methods are quite near the optimal sim s

generalized cesaro difference sequence spaces of non absolute type involving lacunary sequences in this paper we introduce and examine some properties of the sequence spaces c d v m q p c d v m q p c d v m q p c d v m q p n q d v m p s q d v m and study various properties and inclusion relations of these spaces we also show that the space s q d v m may be represented as n q d v m p space

some generalizations of the space b vp of p bounded variation sequences the spaces bvp and bv of sequences of p bounded variation have recently been introduced by basar and altay f basar b altay on the space of sequences of p bounded variation and related matrix mappings ukrainian math j 55 1 2003 136 147 where 1 p in the present paper the sequence spaces bv u p and bv u p of non absolute type have been defined and it has been proved that the spaces bv u p and bv u p are linearly isomorphic to the spaces l p and l p of maddox respectively besides this the and duals of the spaces bv u p and bv u p have been computed and the basis of the space bv u p has been constructed the classes bv u p l and bv u p c of infinite matrices have been characterized and the characterizations of some other classes have also been derived by means of a given basic lemma the final section of the paper has been devoted to some consequences about the rotundity of the space bv u p

on the classes of fractional order difference sequence spaces and their matrix transformations abstract the main purpose of the present article is to introduce the classes of generalized fractional order difference sequence spaces l p c 0 p and c p by defining the fractional difference operator x k i 0 1 i 1 i i 1 x k i where is a positive proper fraction and k n 1 2 3 results concerning the linearity and various topological properties of these spaces are established and also the alpha beta gamma and n duals of these spaces are obtained the matrix transformations from these classes into maddox spaces are also characterized throughout the article we use the notation n as the gamma function of n defined by an improper integral n 0 e t t n 1 dt where n 0 1 2 and n 1 n n

matrix transformations on some sequence spaces related to strong cesaro summability and boundedness the spaces a 0 r d a c r d and a r d introduced by aydin and basar c aydin f basar some new difference sequence spaces appl math comput 157 3 2004 677 693 can be considered as the matrix domains of a triangle in the sets of all sequences that are summable to zero summable and bounded by the cesaro method of order 1 here we define the sets of sequences which are the matrix domains of that triangle in the sets of all sequences that are summable summable to zero or bounded by the strong cesaro method of order 1 with index p 1 we determine the b duals of the new spaces and characterize matrix transformations on them into the sets of bounded convergent and null sequences

the matrix domain and the spectra of a generalized difference operator abstract in this paper some results of the generalized difference operator b v m are studied the euler difference sequence spaces e 0 t b v m and e c t b v m are introduced furthermore some functional properties and duals of these sequence spaces are examined finally the sets of the spectrum the point spectrum the residual spectrum and the continuous spectrum of the operator b v m on the space l 1 are given

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

some new spaces of double sequences abstract in this study we define the double sequence spaces bs bs t cs p cs b p cs r and bv and also examine some properties of those sequence spaces furthermore we show that these sequence spaces are complete paranormed or normed spaces under some certain conditions we determine the duals of the spaces bs bv cs b p and the duals of the spaces cs b p and cs r of double series finally we give the conditions which characterize the class of four dimensional matrix mappings defined on the spaces cs b p cs r and cs p of double series

on a matrix identity connecting iteration operators associated with a p cyclic matrix the successive overrelaxation sor and the symmetric sor ssor iteration matrices are connected with the jacobi iteration matrix in case these operators are associated with a 9 p 9 generalized consistently ordered matrix through certain matrix identities the validity of these identities has been proved in the last couple of years very recently an analogous matrix identity was shown to hold for the modified sor msor and the jacobi iteration matrices in the particular cases p 9 2 l 3 1 and 3 2 it is the main objective of this paper to extend the validity of this identity to cover an entire class or pairs p 9 the identity in question is not only of theoretical interest but of practical importance too since it can be used to show the equivalence of the msor and a class of p step iterative methods for the solution of a linear system whose matrix coefficient possesses the 9 p q generalized consistently ordered property

on matrix domains of triangles we prove some general results for the determination of the duals of and the characterisations of matrix transformations on matrix domains of arbitrary triangles in fk spaces our results contain almost all recently published ones as special cases we also study the measure of noncompactness of several matrix transformations in particular we obtain some known results of sember give the corrected version of a recent result by djolovic and study compact operators on some spaces of altay basar and mursaleen

generic frechet differentiability of the pressure in certain lattice systems this note has two goals the first is to give an explicit description theorem 1 of the duals of certain weighted products h of a countable family of banach spaces these products include the usual spaces of interactions which arise in statistical mechanics the second goal is to use this description to prove that if the factor spaces are finite dimensional and the weight functionh satisfies a certain growth condition then the pressure is frechet differentiable wherever it is gateaux differentiable hence is frechet differentiable in a denseg subset

some paranormed sequence spaces of non absolute type derived by weighted mean abstract the sequence spaces l p c p and c 0 p were introduced and studied by maddox i j maddox paranormed sequence spaces generated by infinite matrices proc cambridge philos soc 64 1968 335 340 in the present paper the sequence spaces u v p of non absolute type which are derived by the generalized weighted mean are defined and proved that the spaces u v p and p are linearly isomorphic where denotes the one of the sequence spaces l c or c 0 besides this the and duals of the spaces u v p are computed and the basis of the spaces c 0 u v p and c u v p is constructed additionally it is established that the sequence space c 0 u v has ad property and given the f dual of the space c 0 u v p finally the matrix mappings from the sequence spaces u v p to the sequence space and from the sequence space to the sequence spaces u v p are characterized

fields of values and iterative methods abstract the performance of an iterative scheme to solve x t x c t c n n c c n is often judged by spectral properties of t if t is not normal it is however well known that only conclusions about the assymptotic behavior of an iterative method can be drawn from spectral information to anticipate the progress of the iteration after a finite number of steps the knowledge of the eigenvalues alone is often useless in addition the spectrum of t may be highly sensitive to perturbations if t is not normal an iterative method which on the basis of some spectral information is predicted to converge rapidly for t may well diverge if t is slightly perturbed in practice the convergence of the iteration x m t x m 1 c is therefore frequently measured by some norm verbar t verbar rather than by the spectral radius t but apart from the fact that norms lead to error estimates which are often too pessimistic they cannot be used to analyze more general schemes such as e g the chebyshev iterative methods here we discuss another tool to analyze the behavior of an iterative method namely the field of values w t the collection of all rayleigh quotients of t w t contains the eigenvalues of t and the numerical radius t max z w t z defines a norm on c n n the field of values represents therefore an intermediate concept to judge an iterative scheme by it is related to the spectral approach but has also certain norm properties

k step iterative methods for solving nonlinear systems of equations let n n be frechet differentiable and let the equation 1 x phi left x right have at least one fixed point we considerk step stationary iterative methods 2 y m mu 0 phi left y m 1 right mu 1 y m 1 mu k y m k m geqq k with 0 1 k 1 using results for an affine mapping n n it is proven that 2 may converge locally even in cases where the usual iterationx m x m 1 belonging to 1 diverges these results are extended to nonstationary methods of type 2 and to cyclic mappings

some new sequence spaces derived by the domain of the triple band matrix let l denote any of the classical spaces c c 0 and p of bounded convergent null and absolutely p summable sequences respectively and let l b also be the domain of the triple band matrix b r s t in the sequence space l where 1