conditions of regularity in cone metric spaces in this paper we prove some fixed points results on cone metric spaces for maps satisfying general contractive type conditions among other things we extend some results of nguyen 11 from metric spaces to cone metric spaces the example is included

partially ordered cone metric spaces and coupled fixed point results bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 2006 1379 1393 studied the coupled coincidence point of a mapping f from xxx into x and a mapping g from x into x e karapinar e karapinar couple fixed point theorems for nonlinear contractions in cone metric spaces comput math appl 2010 doi 10 1016 j camwa 2010 03 062 proved some results of the coupled coincidence point of a mapping f from xxx into x and a mapping g from x into x over normal cones without regularity in the present paper we prove that coupled coincidence fixed point theorems over cone metric spaces are not necessarily normal our results generalize several well known comparable results in the literature

iterative approximation to a coincidence point of two mappings in this article two methods for approximating the coincidence point of two mappings are studied and moreover rates of convergence for both methods are given these results are illustrated by several examples in particular we apply such results to study the convergence and their rate of convergence of these methods to the solution of a nonlinear integral equation and of a nonlinear differential equation

fixed points of weak contractions in cone metric spaces abstract cone metric spaces are generalizations of metric spaces where the metric is banach space valued weak contractions are generalizations of the banach s contraction mapping which have been studied by several authors in the present work we establish a unique fixed point result for weak contractions in cone metric spaces our result is supported by an example

kkm mappings in cone metric spaces and some fixed point theorems abstract in this paper we define kkm mappings in cone metric spaces and define n cone metric spaces to obtain some fixed point theorems and hence generalize the results obtained in a amini m fakhar j zafarani kkm mapping in metric spaces nonlinear anal 60 2005 1045 1052

coincidence and common fixed and periodic point theorems in cone metric spaces the aim of this paper is to show the existence of coincidence and fixed points for mappings satisfying property e a in cone metric spaces also we give periodic point theorems in cone metric spaces

multivalued f weakly picard mappings recently m berinde and v berinde m berinde v berinde on a general class of multi valued weakly picard mappings j math anal appl in press extended the notion of weak contraction from single valued mappings to multivalued mappings and obtained some convergence theorems for the picard iteration associated with multivalued weak contractions we further extended the notion of weak contraction and introduced the notions of multivalued f weak contraction and generalized multivalued f weak contraction we obtain some coincidence and fixed point theorems our results extend m berinde v berinde on a general class of multi valued weakly picard mappings j math anal appl in press and those contained therein

boyd wong type common fixed point results in cone metric spaces abstract some common fixed point results in cone metric spaces of c di bari and p vetro c di bari p vetro pairs and common fixed points in cone metric spaces rend cir mat palermo 57 2008 279 285 as well as p raja and s m vaezpour p raja s m vaezpour some extensions of banach s contraction principle in complete metric spaces fixed point theory appl 2008 doi 10 1155 2008 768294 are extended using generalized contractive type conditions and cones which may be nonnormal cone metric versions of several well known results such as boyd wong s theorem d w boyd j s wong on nonlinear contractions proc amer math soc 20 1969 458 464 are obtained as special cases

dft calculation of the generalized and drazin inverse of a polynomial matrix a new algorithm is presented for the determination of the a generalized inverse and b drazin inverse of a polynomial matrix the proposed algorithms are based on the discrete fourier transform and thus are computationally fast in contrast to other known algorithms the above algorithms are implemented in the mathematica programming language and illustrated via examples

effective partitioning method for computing generalized inverses and their gradients abstract we extend the algorithm for computing 1 1 3 1 4 inverses and their gradients from 11 to the set of multiple variable rational and polynomial matrices an improvement of this extension appropriate to sparse polynomial matrices with relatively small number of nonzero coefficient matrices as well as in the case when the nonzero coefficient matrices are sparse is introduced for that purpose we exploit two effective structures form 6 which make use of only nonzero addends in polynomial matrices and define their partial derivatives symbolic computational package mathematica is used in the implementation several randomly generated test matrices are tested and the cpu times required by two used effective structures are compared and discussed

the lie poisson structure of integrable classical non linear sigma models the canonical structure of classical non linear sigma models on riemannian symmetric spaces which constitute the most general class of classical non linear sigma models known to be integrable is shown to be governed by a fundamental poisson bracket relation that fits into ther s matrix formalism for non ultralocal integrable models first discussed by maillet the matricesr ands are computed explicitly and being field dependent satisfy fundamental poisson bracket relations of their own which can be expressed in terms of a new numerical matrixc it is proposed that all these poisson brackets taken together are representation conditions for a new kind of algebra which for this class of models replaces the classical yang baxter algebra governing the canonical structure of ultralocal models the poisson brackets for the transition matrices are also computed and the notorious regularization problem associated with the definition of the poisson brackets for the monodromy matrices is discussed

computing generalized inverse of polynomial matrices by interpolation abstract we investigated an interpolation algorithm for computing the moore penrose inverse of a given polynomial matrix based on the leverrier faddeev method also a method for estimating the degrees of polynomial matrices arising from the leverrier faddeev algorithm is given as the improvement of the interpolation algorithm algorithms are implemented in the symbolic programming language mathematica and tested on several different classes of test examples

some common fixed point theorems for a family of mappings in metrically convex spaces abstract in the present paper some common fixed point theorems for a sequence and a pair of nonself mappings in complete metrically convex metric spaces are proved which generalize such results due to khan et al m s khan h k pathak m d khan some fixed point theorems in metrically convex spaces georgian math j 7 3 2000 523 530 assad n a assad on a fixed point theorem of kannan in banach spaces tamkang j math 7 1976 91 94 chatterjea s k chatterjea fixed point theorems c r acad bulgare sci 25 1972 727 730 and several others some related results are also discussed

a common fixed point theorem for compatible quasi contractive self mappings in metric spaces a common fixed point theorem for weakly commuting quasi contractive self mappings with contracting orbital diameters in metric spaces v berinde a common fixed point theorem for quasi contractive type mappings ann univ sci budapest 46 2003 81 90 is extended to the more general class of compatible quasi contractive self mappings our result does extend and generalize numerous related results in literature

computation of the generalized inverse of a polynomial matrix and applications abstract the computation of the generalized inverse of a constant matrix is utilized in finding the generalized inverse and its laurent expansion of a nonregular polynomial matrix the proposed algorithm constitutes a generalization of the algorithm proposed by fragulis et al for regular polynomial matrices and gives rise to numerous applications in multivariable system analysis

common fixed point theorems for a mixed family of fuzzy and crisp mappings we prove a common fixed point theorem for the nonfuzzy mappings and a sequence of fuzzy mappings in a linear metric space under hybrid d compatible condition our result is more general than those of lee et al fuzzy sets and systems 2000a submitted and many others biologically relevant involvements are raised with respect to brain functioning

coincidence and fixed point theorems for generalized ψ φ weak nonlinear contraction in ordered k metric spaces in this paper we establish coincidence and fixed point theorems for a pair of mappings satisfying a new generalized j f weak nonlinear contraction type condition in ordered k metric spaces the presented results generalize and extend the very recent results of choudhury and metiya b s choudhury and n metiya the point of coincidence and common fixed point for a pair of mappings in cone metric spaces computers and mathematics with applications 60 2010 1686 1695

common fixed point theorems for contractive maps two common fixed point theorems have been proved by using minimal type commutativity and contractive conditions the last theorem extends known results on compatible maps to a wider class of mappings

cone metric spaces and fixed point theorems of contractive mappings in this paper we introduce cone metric spaces prove some fixed point theorems of contractive mappings on cone metric spaces

common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces in the first part of this paper we generalize results on common fixed points in ordered cone metric spaces obtained by i altun and g durmaz i altun g durmaz some fixed point theorems on ordered cone metric spaces rend circ mat palermo 58 2009 319 325 and i altun b damnjanovic and d djoric i altun b damnjanovic d djoric fixed point and common fixed point theorems on ordered cone metric spaces appl math lett 2009 doi 10 1016 j aml 2009 09 016 by weakening the respective contractive condition then the notions of quasicontraction and g quasicontraction are introduced in the setting of ordered cone metric spaces and respective common fixed point theorems are proved in such a way known results on quasicontractions and g quasicontractions in metric spaces and cone metric spaces are extended to the setting of ordered cone metric spaces examples show that there are cases when new results can be applied while old ones cannot

from geometric quantization to conformal field theory investigation of 2d conformal field theory in terms of geometric quantization is given we quantize the so called model space of the compact lie group virasoro group and kac moody group in particular we give a geometrical interpretation of the virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of cft minimal models 2d gravity wznw theory in the appendix we discuss the relation between classical constant r matrices and this geometrical approach

an efficient matrix iteration for computing weighted moore penrose inverse the goal of this study is threefold in order to calculate the weighted moore penrose inverse we first derive a new matrix iteration for computing the inverse of non singular square matrices we then analytically extend the obtained results so as to compute the moore penrose generalized inverse of a non square matrix subsequently these results will again be theoretically extended to find the weighted moore penrose inverse the computational efficiency of the presented scheme is rigourously studied and compared with the existing matrix iterations to show that it is economic some applications are given as well

common fixed points for g f type maps in cone metric spaces abstract in this paper we study common fixed points for the self and non self g f type maps in cone metric spaces our main results are related to the cases when g is f quasi contraction in a sense of das and naik and the cone need not be normal these results generalize several well known comparable results in the literature

approximation of point of coincidence and common fixed points of quasi contraction mappings using the jungck iteration scheme let x d be a cone metric space over a solid vector space y in this paper we prove a convergence theorem with error estimates and localization formula for jungck iteration process for approximating points of coincidence and common fixed points of two selfmappings t and f of x satisfying a quasi contraction condition of the type d t x t y co d f x f y d f x t x d f y t y d f x t y d f y t x for all x y x where 0 1 is a constant our result complements the recent result of ding et al 9 the main result is new even in the classical metric space setting moreover this result answers an open question posed by olaleru 17 concerning common fixed points in metric spaces

invariant approximations and r subweakly commuting maps the existence of invariant approximations for r subweakly commuting mappings is proved our results extend most of the known results to a new class of noncommuting mappings

ordered cone metric spaces and fixed point results in this paper we introduce a partial order on a cone metric space and prove a caristi type theorem furthermore we prove fixed point theorems for single valued nondecreasing and weakly increasing mappings and multi valued mappings on an ordered cone metric space

the algorithm for computing the drazin inverses of two variable polynomial matrices we propose a finite algorithm for computing drazin inverse of two variable polynomial matrices based on greville s finite algorithm for computing drazin inverse of a constant matrix also a three dimensional recursive algorithm to do that is deduced examples show that these methods are feasible and the implementation is developed in the symbolic package matlab

symbolic computation of weighted moore penrose inverse using partitioning method abstract we propose a method and algorithm for computing the weighted moore penrose inverse of one variable rational matrices continuing this idea we develop an algorithm for computing the weighted moore penrose inverse of one variable polynomial matrix these methods and algorithms are generalizations of the method for computing the weighted moore penrose inverse for constant matrices originated in wang and chen g r wang y l chen a recursive algorithm for computing the weighted moore penrose inverse a mn j comput math 4 1986 74 85 and the partitioning method for computing the moore penrose inverse of rational and polynomial matrices introduced in stanimirovic and tasic p s stanimirovic m b tasic partitioning method for rational and polynomial matrices appl math comput 155 2004 137 163 algorithms are implemented in the symbolic computational package mathematica

common coupled fixed point theorems in cone metric spaces for w compatible mappings in this paper we introduce the concept of a w compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in cone metric space with a cone having non empty interior coupled common fixed point theorems for such mappings are also proved our results generalize extend and unify several well known comparable results in the literature results are supported by three examples

common fixed points under contractive conditions in cone metric spaces the aim of this paper is to present coincidence point result for two mappings in cone metric space which satisfy new contractive conditions our results generalize fixed point theorems of jungck g jungck commuting maps and fixed points amer math monthly 83 1976 261 263 abbas jungck m abbas g jungck common fixed point results for noncommuting mappings without continuity in cone metric spaces j math anal appl 341 2008 416 420 and fisher b fisher four mappings with a common fixed point arabic summary j univ kuwait sci 8 1981 131 139 in cone metric spaces to symmetric spaces

the point of coincidence and common fixed point for a pair of mappings in cone metric spaces in this paper the existence of a point of coincidence and a common fixed point for two weakly compatible maps on a cone metric space has been established the two mappings are assumed to satisfy certain weak inequalities supporting examples are also given

a common fixed point theorem for r weakly commuting mappings in probabilistic spaces with nonlinear contractive conditions abstract this paper presents a common fixed point theorem for a family of r weakly commuting mappings satisfying nonlinear type contractive conditions this result improves and unifies previous results due to o regan and saadati d o regan r saadati nonlinear contraction theorems in probabilistic spaces appl math comput 195 2008 86 93 also the following results will be probabilistic versions and improvements of the results given in d w boyd j s w wong on nonlinear contractions proc am math soc 20 1969 458 464 g jungck commuting maps and fixed points am math month 83 1976 261 263 r p pant common fixed points of noncommuting mappings j math anal appl 188 1994 436 440 and many other

common fixed point theorems on generalized distance in ordered cone metric spaces in this paper we introduce a concept of the c distance in a cone metric space and by using the concept of the c distance prove some fixed point theorems in ordered cone metric spaces

a finite algorithm for the drazin inverse of a polynomial matrix based on greville s finite algorithm for drazin inverse of a constant matrix we propose a finite numerical algorithm for the drazin inverse of polynomial matrices we also present a new proof for decell s finite algorithm through greville s finite algorithm

a note on cone metric fixed point theory and its equivalence abstract the main aim of this paper is to investigate the equivalence of vectorial versions of fixed point theorems in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense we show that the banach contraction principles in general metric spaces and in t v s cone metric spaces are equivalent our theorems also extend some results in huang and zhang 2007 l g huang x zhang cone metric spaces and fixed point theorems of contractive mappings j math anal appl 332 2007 1468 1476 rezapour and hamlbarani 2008 sh rezapour r hamlbarani some notes on the paper cone metric spaces and fixed point theorems of contractive mappings j math anal appl 345 2008 719 724 and others

on common fixed points in g metric spaces using e a property in this paper we introduce some new types of pairs of mappings f g on g metric spaces called g weakly commuting of type g f and g r weakly commuting of type g f we obtain also several common fixed point results by using the e a property

computation of the inverse of a polynomial matrix and evaluation of its laurent expansion abstract an algorithm is given which constitutes a generalization of the algorithm for the inversion of a pencil se a due to mertzios 1984 in the case of general systems described in differential operator form recursive formulae are obtained for the calculation of both the coefficient matrices of the adjoint of the polynomial matrix as well as for the coefficients of the characteristic polynomial of the polynomial matrix a simple method is also presented that allows the evaluation of the laurent expansion for the inverse of a polynomial matrix of any order specifically an arma model is given for the computation of the coefficient matrices of the laurent expansion in terms of the coefficient matrices of the polynomial matrix without inverting the latter the laurent expansion of a polynomial matrix is used for the analysis and synthesis of the polynomial matrix descriptions that constitute a further generalization of the singular or generalized systems

an accelerated iterative method for computing weighted moore penrose inverse the goal of this paper is to present an accelerated iterative method for computing weighted moore penrose inverse analysis of convergence is included to show that the proposed scheme has sixth order convergence using a proper initial matrix a sequence of iterates will be produced which is convergent to the weighted moore penrose inverse numerical experiments are reported to show the efficiency of the new method

coincidence and common fixed point results in partially ordered cone metric spaces and applications to integral equations abstract in this paper coincidence and common fixed point results are established in a partially ordered cone metric space an application of our results obtained to prove the existence of a common solution to integral equations is presented

quasi contraction of perov type abstract perov 1964 19 used the concept of vector valued metric space and obtained a banach type fixed point theorem on such a complete generalized metric space in this article we study fixed point results for the new extensions of ciric s quasi contraction to cone metric space and we give some generalized versions of the fixed point theorem of perov as corollaries we generalized some results of zima 1992 28 and borkowski et al 2010 4 for a banach space with a non normal cone the theory is illustrated with some examples

common fixed points for banach operator pairs in best approximation the notion of banach operator pairs is introduced as a new class of noncommuting maps some common fixed point theorems for banach operator pairs and the existence of the common fixed points of best approximation are presented these results are proved without the assumption of linearity or affinity for either f or g which shows that the concept about banach operator pairs is potentially useful in the study of common fixed points

on ciric maps with a generalized contractive iterate at a point and fisher s quasi contractions in cone metric spaces in this paper we generalize and unify some results of sehgal and guseman and ciric s theorem for mappings with a generalized contractive iterate at a point to cone metric spaces in which the cone does not need to be normal as corollaries we obtain recent results of huang and zhang and raja and vaezpour furthermore we introduce the definition of fisher quasi contractions on cone metric spaces and study their properties among other things using new method of proof we solve the open problem for the interval of contractive constant l of ciric quasi contraction in non normal cone metric spaces and as sn immediate corollary we recover the recent result of rezapour and hamlbarani

common fixed point theorems of gregus type for weakly compatible mappings satisfying contractive conditions of integral type abstract we prove a common fixed point theorem of gregus type for four mappings satisfying a contractive condition of integral type in metric spaces using the concept of weak compatibility which generalizes theorem 2 of a djoudi l nisse gregus type fixed points for weakly compatible mappings bull belg math soc 10 2003 369 378 and other papers we prove also common fixed point theorems of gregus type using a strict contractive condition of integral type a property e a and a common property e a introduced by m aamri d el moutawakil some new common fixed point theorems under strict contractive conditions j math anal appl 270 2002 181 188 and w liu j wu z li common fixed points of single valued and multi valued maps int j math math sci 19 2005 3045 3055 respectively

generalized φ contraction for a pair of mappings on cone metric spaces using the setting of cone metric space a fixed point theorem is proved for two maps and several corollaries are obtained in these cases the cone does not need to be normal these results generalize several well known compatible recent and classical results in the literature as an application the existence of solution of an integral equation is presented

common fixed point results for noncommuting mappings without continuity in cone metric spaces the existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions without appealing to continuity in a cone metric space is established these results generalize several well known comparable results in the literature

common fixed points for four maps in cone metric spaces the existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein in a cone metric space is proved these results extend unify and generalize several well known comparable results in the existing literature

on cone metric spaces a survey abstract using an old m krein s result and a result concerning symmetric spaces from s radenovic z kadelburg quasi contractions on symmetric and cone symmetric spaces banach j math anal 5 1 2011 38 50 we show in a very short way that all fixed point results in cone metric spaces obtained recently in which the assumption that the underlying cone is normal and solid is present can be reduced to the corresponding results in metric spaces on the other hand when we deal with non normal solid cones this is not possible in the recent paper m a khamsi remarks on cone metric spaces and fixed point theorems of contractive mappings fixed point theory appl 2010 7 pages article id 315398 doi 10 1115 2010 315398 the author claims that most of the cone fixed point results are merely copies of the classical ones and that any extension of known fixed point results to cone metric spaces is redundant also that underlying banach space and the associated cone subset are not necessary in fact khamsi s approach includes a small class of results and is very limited since it requires only normal cones so that all results with non normal cones which are proper extensions of the corresponding results for metric spaces cannot be dealt with by his approach

fixed point theorems in fuzzy metric spaces using property e a abstract we prove two common fixed point theorems for a pair of weakly compatible maps in fuzzy metric spaces both in the sense of kramosil and michalek and in the sense of george and veeramani by using e a property

approximation of common fixed points of weakly compatible pairs using the jungck iteration abstract we show that the jungck iteration scheme can be used to approximate the common fixed points of some weakly compatible pairs of generalized quasicontractive operators defined on metric spaces the existence of coincidence points are also discussed for those pair of maps the results are generalizations of well known results of the convergence of picard iterations for single self maps of banach spaces in particular the results improve generalize and extend the recent results of berinde v berinde a common fixed point theorem for compatible quasi contractive self mappings in metric spaces applied mathematics and computation 213 2009 348 354 and answers the open question posed in the paper

partitioning method for rational and polynomial matrices we propose an extension of the grevile s partitioning method for computing the moore penrose inverse which is applicable to the set of rational matrices also we develop an algorithm for computing the moore penrose inverse of given one variable polynomial matrix which is based on the grevile s method major problems arising in the implementation of this method are repetitive recomputations of the same values and simplification of rational and polynomial expressions which contain unknown variable these algorithms are implemented in the symbolic computational package mathematica

fixed point theorems for families of weakly non expansive maps abstract in this paper we present some fixed point theorems for families of weakly non expansive maps under some relatively weaker and more general conditions our results generalize and improve several results due to jungck g jungck fixed points via a generalized local commutativity int j math math sci 25 8 2001 497 507 jachymski j jachymski a generalization of the theorem by rhoades and watson for contractive type mappings math japon 38 6 1993 1095 1102 guo c guo an extension of fixed point theorem of krasnoselski chinese j math p o c 21 1 1993 13 20 rhoades b e rhoades a comparison of various definitions of contractive mappings trans amer math soc 226 1977 257 290 and others

fixed point theorem for two non self mappings in cone metric spaces in this paper we extend a fixed point theorem of imdad and kumar for a pair of non self maps to non normal cone spaces

a finite algorithm for generalized inverses of polynomial and rational matrices there are proposed two types of finite algorithms for symbolic computation of outer inverses of a given polynomial or rational matrix based on the extension of the leverrier faddeev algorithm the implementation of the algorithm corresponding to rational matrices is developed in the symbolic package mathematica

some common fixed point theorems for banach operator pairs with applications in best approximation abstract the ordered pair t i of two self maps of a metric space x d is called a banach operator pair if the set f i of fixed points of i is t invariant i e t f i f i some common fixed point theorems for a banach operator pair and the existence of common fixed points of best approximation are presented in this paper the results prove generalize and extend some results of al thagafi m a al thagafi common fixed points and best approximation j approx theory 85 1996 318 323 carbone a carbone applications of fixed point theorems jnanabha 19 1989 149 155 chen and li j chen z li common fixed points for banach operator pairs in best approximations j math anal appl 336 2007 1466 1475 habiniak l habiniak fixed point theorems and invariant approximation j approx theory 56 1989 241 244 jungck and sessa g jungck s sessa fixed point theorems in best approximation theory math japon 42 1995 249 252 sahab khan and sessa s a sahab m s khan s sessa a result in best approximation theory j approx theory 55 1988 349 351 shahzad n shahzad invariant approximations and r subweakly commuting maps j math anal appl 257 2001 39 45 and of few others

abstract metric spaces and sehgal guseman type theorems recently raja and vaezpour p raja and s m vaezpour some extensions of banach s contraction principle in complete cone metric spaces fixed point theory appl 2008 11 pages doi 10 1155 2008 768294 article id 768294 proved some results for sehgal guseman type theorems in the framework of abstract cone metric spaces over a normal solid cone the purpose of this paper is to present this in the framework of symmetric spaces which are associated with abstract cone metric spaces introduced by radenovic and kadelburg s radenovic z kadelburg quasi contractions on symmetric and cone symmetric spaces isi j bjma electronic in press our results extend and generalize sehgal guseman type theorems from metric and abstract metric spaces to some symmetric spaces examples are given to illustrate the results

coincidence and fixed points in symmetric spaces under strict contractions abstract some common fixed point theorems due to aamri and el moutawakil m aamri d el moutawakil some new common fixed point theorems under strict contractive conditions j math anal appl 270 2002 181 188 and pant and pant r p pant v pant common fixed points under strict contractive conditions j math anal appl 248 2000 327 332 proved for strict contractive mappings in metric spaces are extended to symmetric semi metric spaces under tight conditions some related results are derived besides discussing illustrative examples which establish the utility of results proved in this note

effective partitioning method for computing weighted moore penrose inverse we introduce a method and an algorithm for computing the weighted moore penrose inverse of multiple variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices these methods and algorithms are generalizations of algorithms developed in m b tasic p s stanimirovic m d petkovic symbolic computation of weighted moore penrose inverse using partitioning method appl math comput 189 2007 615 640 to multiple variable rational and polynomial matrices and improvements of these algorithms on sparse matrices also these methods are generalizations of the partitioning method for computing the moore penrose inverse of rational and polynomial matrices introduced in p s stanimirovic m b tasic partitioning method for rational and polynomial matrices appl math comput 155 2004 137 163 m d petkovic p s stanimirovic symbolic computation of the moore penrose inverse using partitioning method internat j comput math 82 2005 355 367 to the case of weighted moore penrose inverse algorithms are implemented in the symbolic computational package mathematica

nonlinear ψ quasi contractions of ciric type in partial metric spaces abstract in this paper we obtain results of fixed and common fixed points for self mappings satisfying a nonlinear contractive condition of ciric type in the framework of partial metric spaces we also prove results of fixed point for self mappings satisfying an ordered nonlinear contractive condition in the setting of ordered partial metric spaces

banach operator pair and common fixed points for nonexpansive maps abstract let x be a normed space and t and i be two nonexpansive self maps on the closed convex subset c x it is proved that if i t is a banach operator pair and t c is compact then f i t 0 a family of nonexpansive maps is also investigated the well known de marr s fixed point theorem is extended to the noncommuting case by introducing a notion of banach operator family as an application of the theorem the problem for the common fixed point in invariant approximation for convex set is solved directly in a quite different way from the others before

common fixed point theorems for c distance in ordered cone metric spaces abstract recently cho et al y j cho r saadati s h wang common fixed point theorems on generalized distance in ordered cone metric spaces comput math appl 61 2011 1254 1260 introduced the concept of the c distance in a cone metric space and established some fixed point theorems on c distance the aim of this paper is to extend and generalize the main results of cho et al 20 and also show some examples to validate our main results

approximation of fixed points of uniformly r subweakly commuting mappings we introduce a new class of uniformly r subweakly commuting mappings and then using this class study the problem of approximation of common fixed points of asymptotically s nonexpansive mappings in a banach space with uniformly g teaux differentiable norm

symbolic computation of at s 2 inverses using qdr factorization abstract efficient evaluation of the full rank qdr decomposition is established a method and algorithm for efficient symbolic computation of a t s 2 inverses of a given rational matrix a is defined using the full rank qdr decomposition of an appropriate rational matrix w the algorithm is implemented using mathematica s ability to deal with symbolic expressions as well as with numbers examples including polynomial and rational matrices are presented some comparisons with well known methods for symbolic evaluation of generalized inverses are obtained

classical exchange algebra of the superstring on s 5 with ads time a classical exchange algebra of the superstring on s5 with ads time is shown on the light like plane to this end we use the geometrical method of which consistency is guaranteed by the classical yang baxter equation the dirac method does not work since there are constraints in which first class and second class constraints are mixed and one can hardly disentangle with each other keeping the isometry

about the generalized lm inverse and the weighted moore penrose inverse the recursive method for computing the generalized lm inverse of a constant rectangular matrix augmented by a column vector is proposed in udwadia and phohomsiri 2007 16 17 the corresponding algorithm for the sequential determination of the generalized lm inverse is established in the present paper we prove that the introduced algorithm for computing the generalized lm inverse and the algorithm for the computation of the weighted moore penrose inverse developed by wang and chen 1986 in 23 are equivalent algorithms both of the algorithms are implemented in the present paper using the package mathematica several rational test matrices and randomly generated constant matrices are tested and the cpu time is compared and discussed

differentiation of generalized inverses for rational and polynomial matrices our basic motivation is a direct method for computing the gradient of the pseudo inverse of well conditioned system with respect to a scalar proposed in 13 by layton in the present paper we combine the layton s method together with the representation of the moore penrose inverse of one variable polynomial matrix from 24 and developed an algorithm for computing the gradient of the moore penrose inverse for one variable polynomial matrix moreover using the representation of various types of pseudo inverses from 26 based on the grevile s partitioning method we derive more general algorithms for computing 1 1 3 and 1 4 inverses of one variable rational and polynomial matrices introduced algorithms are implemented in the programming language mathematica illustrative examples on analytical matrices are presented

fixed point theory in cone metric spaces obtained via the scalarization method motivated by the scalarization method in vector optimization theory we take a new approach to fixed point theory on cone metric spaces by using our method we prove some fixed point theorems and several common fixed point theorems on cone metric spaces in which the cone need not be normal our results improve and generalize many well known results from the literature