stability of cauchy jensen type functional equation in generalized fuzzy normed spaces in this paper we establish some stability results concerning the cauchy jensen functional equation in generalized fuzzy normed spaces the results of the present paper improve and extend some recent results

generalized quadratic mappings of r type in several variables let x y be vector spaces it is shown that if an even mapping f x y satisfies f 0 0 and 2cl 1d 2 cld 2 cl 2d 2 r2f j 1dxjr j 0 1 j 1d j lr2f j 1d 1 j xjr cld 1 cl 1d 1 2d 2cl 1 cld 2 cl 2d 2 j 1df xj for all x1 xd x then the even mapping f x y is quadratic furthermore we prove the cauchy rassias stability of the functional equation in banach spaces

homotopy of unitaries in simple c algebras with tracial rank one let 0 be a positive number is there a number 0 satisfying the following given any pair of unitaries u and v in a unital simple c algebra a with v 0 in k1 a for which uv vu there is a continuous path of unitaries v t t 0 1 a such that v 0 v v 1 1and uv t v t u for allt 0 1 an answer is given to this question when a is assumed to be a unital simple c algebra with tracial rank no more than one let c be a unital separable amenable simple c algebra with tracial rank no more than one which also satisfies the uct suppose that c a is a unital monomorphism and suppose that v a is a unitary with v 0 in k1 a such that v almost commutes with it is shown that there is a continuous path of unitaries v t t 0 1 in a with v 0 v and v 1 1 such that the entire path v t almost commutes with provided that an induced bott map vanishes other versions of the so called basic homotopy lemma are also presented

ulam stability problem for generalized a quadratic mappings abstract it is the purpose of this paper to investigate the stability problem of ulam for an approximate mapping for the following generalized quadratic functional equation i 1 n q j i x j n 1 x i n q i 1 n x i n 2 i 1 n q x i for all x i i 1 n where n 1

k homology asymptotic representations and unsuspended e theory connes and higson defined a bivariant homology theory e a b for separable c algebras the elements of e a b are taken to be homotopy classes of asymptotic momorphisms from sa k to sb k in symbols e a b sa sb k if a is k nuclear then e theory agrees with kasparov s bivariant k theory we show that in many cases one need not take suspensions to calculate the e theory group e a b for many a we show e a b a b k for all b among the a for which this is true are c0 x pt for x with the homotopy type of a finite connected cw complex this gives a concrete realization of k homology related to the brown douglas fillmore description for example k0 x arises as asymptotic representations k0 x c0 x k other a for which our isomorphic holds include the nonunital dimension drop intervals in this case there is no distinction between homomorphisms and asymptotic morphisms so we have succeeded in classifying all homomorphisms from a dimension drop interval to a stable c algebra this was subsequently used by elliott j reine angew math 443 1993 179 219 in the classification of certain c algebras the dimension drop interval may also be used to describe k x z n in terms of paths of asymptotic representations of c0 x

on the hyers ulam rassias stability of generalized quadratic mappings in banach modules we prove the generalized hyers ulam rassias stability of generalized a quadratic mappings of type p in banach modules over a banach algebra and of generalized a quadratic mappings of type r in banach modules over a banach algebra

approximation by unitaries with finite spectrum in purely infinite c algebras abstract we prove that a unital purely infinite simple c algebra has c exponential rank at most 1 and therefore has the property weak fu every element of the identity component of the unitary group is norm limit of unitaries with finite spectrum we also prove that the appropriate modification of this statement for nonunital algebras

switching regression models and fuzzy clustering a family of objective functions called fuzzy c regression models which can be used too fit switching regression models to certain types of mixed data is presented minimization of particular objective functions in the family yields simultaneous estimates for the parameters of c regression models together with a fuzzy c partitioning of the data a general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed the approach is illustrated by two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models

extensions of c x by simple c algebras of real rank zero let ext c x a be the set of unitarily equivalence classes of essential c algebra exten sions of the following form 0 a e c x 0 where a is a nonunital separable simple c algebra of real rank zero stable rank one with unique normalized trace and x is a finite cw complex we show that there is a bijection ext c x a kk c x m a a where m a is the multiplier algebra of a in particular we determine when an extension is actually splitting we also in a more general setting give a condition when an essential extension is quasidiagonal 0 introduction we study essential extensions of the following form 0 a f c x 0 where a is a j unital nonunital simple c algebra of real rank zero and stable rank one and x is finite cw complex the brown douglas fillmore bdf theory bdf1 and bdf2 gives a classification of these extensions up to unitary equivalence in the case that a k the c algebra of compact operators on an infinite dimensional separable hubert space since then the theory of c algebra extensions developed rapidly it is very difficult to give a complete list we refer the reader to bl for references while using of theory ext c x a have been computed for the most interesting cases however ext c x a does not provide enough information in general to classify extensions up to unitary equivalence in fact as shown in ln6 and lnl2 there are usually many different unitary equivalence classes of trivial extensions and an extension r with r 0 in ext c x a may not be trivial we will only consider simple c algebras that share some properties with c we consider only those with real rank zero stable rank one and unique quasi trace up to scalar multiples there is an additional property that c has namely its corona algebra m k k the calkin algebra is simple we also as sume that m a a is simple it has been studied when a nonunital but cr unital simple c algebra a has the property that m a a is simple see lnl rrl and zh2 etc it is shown in lnl that a simple c algebra a has the property that m a a is simple if and only if a has continuous scale

c algebras generated by stable relations abstract presentations of certain c algebras such as c0 0 1 mn by generators and relations are proven to be stable by the weakest definition of stability a set p1 pn of star polynomials is stable if operators a1 an which almost satisfy these relations meaning pi a1 an can be perturbed within c a1 an to satisfy these relations exactly homotopy and perturbation results for these c algebras are corollaries in particular we prove some new results about the dimension drop c algebras a n c 0 1 m n 0 1 c i we show that an is semiprojective answering a question of effros and kaminker also we show that whenever an b is a homomorphism approximately contained in a sub c algebra b0 b there is a nearby homomorphism of an into b0 this answers a question raised by elliott we prove technical results regarding mn c0 0 1 which should be useful elsewhere first we show this is projective meaning a star homomorphism mn c0 0 1 b j always lifts to a star homomorphism mn c0 0 1 b secondly we show that for a finitely generated m n a m n c 0 0 1 c 0 0 1 a if the amalgamation is done properly

the stability of the additive cauchy functional equation in non archimedean fuzzy normed spaces a stability result for the additive cauchy functional equation in non archimedean fuzzy normed spaces over a field with valuation is given by using the concept of countable extension of a t norm

a geometric approach of the generalized d alembert equation abstract by using a geometric approach we prove that the set of solutions of the generalized d alembert equation n log f x 1 x n 0 considered in domain of the x1 xn space r n is larger than the set of the functions that can be represented in the form as f x1 xn f1 x2 xn fn x1 xn 1

on the generalized hyers ulam rassias stability in banach modules over a c algebra abstract in this paper we will investigate the generalized hyers ulam rassias stability of an n dimensional quadratic functional equation in banach modules over a c algebra and unitary elements

hyers ulam stability of a generalized apollonius type quadratic mapping abstract let x y be linear spaces it is shown that if a mapping q x y satisfies the following functional equation 0 1 q i 1 n z i i 1 n x i q i 1 n z i i 1 n y i 1 2 q i 1 n x i i 1 n y i 2 q i 1 n z i i 1 n x i i 1 n y i 2 then the mapping q x y is quadratic we moreover prove the hyers ulam stability of the functional equation 0 1 in banach spaces

the generalized hyers ulam rassias stability of a cubic functional equation abstract in this paper we obtain the general solution and the generalized hyers ulam stability for a cubic functional equation f 2x y f 2x y 2f x y 2f x y 12f x

the problem of s m ulam for approximately multiplicative mappings in the present paper we study the problem of s m ulam for approximately multiplicative mappings and we consider new open problems

fuzzy stability of a functional equation associated with inner product spaces moslehian et al investigated the fuzzy stability problems for the cauchy additive functional equation and the jensen additive functional equation in fuzzy banach spaces in this paper we prove the generalized hyers ulam stability of a functional equation associated with inner product spaces in fuzzy banach spaces

stability of a mixed functional equation in several variables on banach modules abstract in this paper we establish the general solution of the functional equation i 1 n f x i 1 n j 1 n x j i 1 n f x i n f 1 n i 1 n x i n 2 and use a fixed point method to prove its generalized hyers ulam stability in banach modules over a unital banach algebra

on algebraic problems behind the brouwer degree of equivariant maps abstract given a finite group g and two unitary g representations v and w possible restrictions on topological degrees of equivariant maps between representation spheres s v and s w are usually expressed in a form of congruences modulo the greatest common divisor of lengths of orbits in s v denoted by v effective applications of these congruences is limited by answers to the following questions i under which conditions is v 1 and ii does there exist an equivariant map with the degree easy to calculate in the present paper we address both questions we show that v 1 for each irreducible non trivial c g module if and only if g is solvable this provides a new solvability criterion for finite groups for non solvable groups we use 2 transitive actions to construct complex representations with non trivial characteristic regarding the second question we suggest a class of norton algebras without 2 nilpotents giving rise to equivariant quadratic maps which admit an explicit formula for the degree

fuzzy bounded linear operators in this paper a notion of boundedness of a linear operator from a fuzzy normed linear space to another fuzzy normed linear space is introduced and two types strong and weak of fuzzy bounded linear operators are defined relation between fuzzy continuity and fuzzy boundedness is studied definitions of fuzzy bounded linear functionals are given and the notions of fuzzy dual spaces are developed the hahn banach theorem the open mapping theorem the closed graph theorem and the uniform boundedness principle theorem are established

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

generalized hyers ulam rassias stability of n sesquilinear quadratic mappings on banach modules over c algebras assume that x is a left banach module over a unital c algebra a it is shown that almost every n sesquilinear quadratic mapping h xxxxx n a is an n sesquilinear quadratic mapping when h rx y z 1 z n h x ry z 1 z n h x y rz 1 z 2 z n h x y z 1 z 2 rz n rh x y z 1 z 2 z n r 0 r 1 holds for all x y z 1 z email protected x moreover we prove the generalized hyers ulam rassias stability of an n sesquilinear quadratic mapping on a left banach module over a unital c algebra

harmonic degree 1 maps are diffeomorphisms lewy s theorem for curved metrics in 1936 h lewy showed that the jacobian determinant of a harmonic homeomorphism between planar domains does not vanish and thus the map is a diffeomorphism this built on the earlier existence

on the cauchy rassias stability of a generalized additive functional equation let x and y be banach spaces and f x y an odd mapping we solve the following generalized additive functional equation rf j 1dxjr j 0 1 j 1d j lrf j 1d 1 j xjr cld 1 cl 1d 1 1 j 1df xj for all x1 xd x moreover we deal with the above functional equation in banach modules over a c algebra and obtain generalizations of the cauchy rassias stability the concept of cauchy rassias stability for the linear mapping was originated from th m rassias s stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

generalized additive mapping in banach modules and isomorphisms between c algebras abstract let x y be vector spaces it is shown that if an odd mapping f x y satisfies the functional equation 1 r f j 1 d x j r j 0 1 j 1 d j l r f j 1 d 1 j x j r c l d 1 c l 1 d 1 1 j 1 d f x j then the odd mapping f x y is additive and we prove the hyers ulam stability of the functional equation 1 in banach modules over a unital c algebra as an application we show that every almost linear bijection h a b of a unital c algebra a onto a unital c algebra b is a c algebra isomorphism when h 2 n r n u y h 2 n r n u h y for all unitaries u a all y a and n 0 1 2

on the hyers ulam stability of linear mappings abstract let e1 be a real normed vector space and e2 a real banach space s m ulam posed the problem when does a linear mapping near an approximately linear mapping e1 e2 exist we give a new generalized solution to this problem an example illustrates when the answer to this question is negative the behaviour of bounded approximately additive mappings which do not satisfy hyers uiam stability is also investigated

on the stability of the linear mapping in banach modules abstract we prove the generalized hyers ulam rassias stability of the linear mapping in banach modules over a unital banach algebra

classifying c algebras with both finite and infinite subquotients abstract we give a classification result for a certain class of c algebras a over a finite topological space x in which there exists an open set u of x such that u separates the finite and infinite subquotients of a we apply our results to c algebras arising from graphs

a semi supervised regression model for mixed numerical and categorical variables in this paper we develop a semi supervised regression algorithm to analyze data sets which contain both categorical and numerical attributes this algorithm partitions the data sets into several clusters and at the same time fits a multivariate regression model to each cluster this framework allows one to incorporate both multivariate regression models for numerical variables supervised learning methods and k mode clustering algorithms for categorical variables unsupervised learning methods the estimates of regression models and k mode parameters can be obtained simultaneously by minimizing a function which is the weighted sum of the least square errors in the multivariate regression models and the dissimilarity measures among the categorical variables both synthetic and real data sets are presented to demonstrate the effectiveness of the proposed method

classification of certain infinite simple c algebras the class of c algebras that arise as the crossed product of a stable simple af algebra with a z action determined by an automorphism which maps a projection in the algebra onto a proper subprojection is proved to consist of simple purely infinite c algebras and a specific subclass of it is proved to be classified by k theory this subclass is large enough to exhaust all possible k groups if g0 and g1 are countable abelian groups with g1 torsion free as it must be then there is a c algebras a in the classified subclass with k0 a g0 and k 1 a g1 the subclass contains the cuntz algebras o with n even and the cuntz krieger algebras o a with k0 o a of finite old order and it is closed under forming inductive limits the c algebras in the classified subclass can be viewed as classifiable models in a strong sense of general simple purely infinite c algebras with the same k theory

stability of mixed additive quadratic jensen type functional equation in various spaces in this paper we prove the generalized hyers ulam stability of the following mixed additive quadratic functional equation 2f x y2 f x y2 f y x2 f x f y in various spaces

generalized quadratic mappings in several variables abstract let x y be vector spaces it is shown that if an even mapping f x y satisfies f 0 0 and 0 1 2 d 2 c l 1 d 2 c l d 2 c l 2 f j 1 d x j j 0 1 j 1 d j l f j 1 d 1 j x j d 1 c l d 1 c l 1 2 d 2 c l 1 d 2 c l d 2 c l 2 j 1 d f x j for all x1 xd x then the even mapping f x y is quadratic furthermore we prove the cauchy rassias stability of the functional equation 0 1 in banach spaces

fuzzy versions of hyers ulam rassias theorem we introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces more precisely we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

a universal multicoefficient theorem for the kasparov groups that holds in the same generality as the universal coefficient theorem of rosenberg and schochet there are advantages in some circumstances to using hom k a k b in place of kk a b these advantages derive from the fact that k a can be equipped with order and scale structures similar to those on k0 a with this additional structure the module k a becomes a powerful invariant of c algebras we show that it is a complete invariant for the class of real rank zero ad algebras the ad algebras are a certain kind of approximately subhomogeneous c algebras which may have torsion in k1 ell in addition to classifying these algebras we calculate their automorphism groups up to approximately innerautomorphisms

on the generalized a quadratic mappings associated with the variance of a discrete type distribution abstract in this paper we prove the hyers ulam rassias stability of the following generalized quadratic functional equation of euler lagrange type i 1 n r i q j 1 n r j x i x j i 1 n r i q i 1 n r i x i i 1 n r i 2 i 1 n r i q x i in banach modules over a unital c algebra where n 1 is a positive integer and r i 0 i 1 n is arbitrary given

classification of extensions of classifiable c algebras abstract for a certain class of extensions e 0 b e a 0 of c algebras in which b and a belong to classifiable classes of c algebras we show that the functor which sends e to its associated six term exact sequence in k theory and the positive cones of k 0 b and k 0 a is a classification functor we give two independent applications addressing the classification of a class of c algebras arising from substitutional shift spaces on one hand and of graph algebras on the other the former application leads to the answer of a question of carlsen and the first named author concerning the completeness of stabilized matsumoto algebras as an invariant of flow equivalence the latter leads to the first classification result for nonsimple graph c algebras

separation of fuzzy normed linear spaces abstract this paper deals with hausdorff separation axiom for fuzzy topological spaces the necessary and sufficient condition obtained in the fuzzy vector topology induced by a fuzzy norm is separated properties of separated and non separated fuzzy norms along with examples are studied separation of a fuzzy norm in terms of the ordinary norm it induces and its consequences are characterised separation of quotient fuzzy semi norm is studied

finite dimensional fuzzy normed linear space abstract the concept of a fuzzy normed linear space is introduced it is proved that in a finite dimensional fuzzy normed linear space fuzzy norms are the same upto fuzzy equivalence finite dimensional fuzzy subspaces of a fuzzy normed linear space are proved to be necessarily complete fuzzy normed linear spaces

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

harmonic diffeomorphisms between the annuli with rotational symmetry abstract we give some necessary and sufficient conditions for the existence of rotationally symmetric harmonic diffeomorphism between the annuli with poincare metric or euclidean metric on the target respectively

modified trif s functional equations in banach modules over a c algebra and approximate algebra homomorphisms abstract we prove the hyers ulam rassias stability of modified trif s functional equations in banach modules over a unital c algebra it is applied to show the stability of banach algebra homomorphisms between banach algebras associated with modified trif s functional equations in banach algebras

variational problem of some quadratic functionals in complex analysis suppose we are given a pair of marked closed riemann surfacess twith the same genus we minimize the modified dirichlet integral for mappings ofsontot which is endowed with some weight in terms of conformal metric on the target surfacet in this paper it is demonstrated that the minimal harmonic map exists and it proves to be teichmuller

harmonic maps between surfaces and teichmuller spaces we study harmonic maps between two distinct compact riemann surfaces of the same genus our aim is to examine the role of the curvature in the relationship between energies of harmonic maps and conformal metrics on the target surface we consider the energy of the energy minimizing map between the surfaces as a function of the metrics within the conformal class of the target and solve the variational problem of minimizing this functional when we restrict the upper curvature bound and normalize the area of the metrics in doing so we show that the upper curvature bound on the normalized target metric is an obstruction in obtaining a degree 1 conformal harmonic map between distinct riemann surfaces

on fuzzy approximately cubic type mapping in fuzzy banach spaces abstract the first study of the fuzzy approximately cubic mappings in nonlinear analysis is due to mirmostafaee and moslehian 2008 and a fuzzy version of a generalized hyers ulam rassias type stability for the cubic functional equation in the fuzzy normed linear space setting is presented in this note we give an alternative proof of this result using the fixed point method in probabilistic metric spaces moreover we investigate fuzzy generalized hyers ulam rassias stability of an n dimensional cubic type functional equation in fuzzy banach spaces

the automorphism group of a simple tracially ai algebra the structure of the automorphism group of a simple tai algebra is studied in particular we show that frac overline rm inn a overline rm inn 0 a is isomorphic as a topological group to an inverse limit of discrete abelian groups for a unital simple ah algebra with bounded dimension growth consequently frac overline rm inn a overline rm inn 0 a is totally disconnected

fuzzy stability of the jensen functional equation we establish a generalized hyers ulam rassias stability theorem in the fuzzy sense in particular we introduce the notion of fuzzy approximate jensen mapping and prove that if a fuzzy approximate jensen mapping is continuous at a point then we can approximate it by an everywhere continuous jensen mapping as a fuzzy version of a theorem of schwaiger we also show that if every fuzzy approximate jensen type mapping from the natural numbers into a fuzzy normed space can be approximated by an additive mapping then the fuzzy norm is complete

lie homomorphisms between lie c algebras and lie derivations on lie c algebras abstract we prove the generalized hyers ulam rassias stability of lie homomorphisms in lie c algebras and of lie derivations on lie c algebras

almost commuting unitary elements in purely infinite simple c algebras we consider the problem whether a pair of almost commuting unitaries selfadjoints is close to a pair of commuting unitaries selfadjoints it is an old problem see hi psh bo v1 v2 d bd ch lorl exli exl2 de lin4 etc dan voiculescu showed in v2 that there is a positive number d and a sequence of commuting unitary matrices un and v with i u v v u ji o

a fuzzy k modes algorithm for clustering categorical data this correspondence describes extensions to the fuzzy k means algorithm for clustering categorical data by using a simple matching dissimilarity measure for categorical objects and modes instead of means for clusters a new approach is developed which allows the use of the k means paradigm to efficiently cluster large categorical data sets a fuzzy k modes algorithm is presented and the effectiveness of the algorithm is demonstrated with experimental results

existence of energy minimal diffeomorphisms between doubly connected domains the paper establishes the existence of homeomorphisms between two planar domains that minimize the dirichlet energy

stability for the functional equation of cubic type abstract in this article we establish the stability of the orthogonally cubic type functional equation 1 2 for all x 1 x 2 x 3 with x i x j i j 1 2 3 where is the orthogonality in the sense of ratz and investigate the stability of the n dimensional cubic type functional equation 1 3 where n 3 is an integer

an approximate universal coefficient theorem an approximate universal coefficient theorem auct for certain c algebras is established we present a proof that kirchberg phillips s classification theorem for separable nuclear purely infinite simple c algebras is valid for c algebras satisfying the auct instead of the uct it is proved that two versions of auct are in fact the same we also show that c algebras that are locally approximated by c algebras satisfying the auct satisfy the auct as an application we prove that certain simple c algebras which are locally type i are in fact isomorphic to simple ah algebras as another application we show that a sequence of residually finite dimensional c algebras which are asymptotically nuclear and which asymptotically satisfies the auct can be embedded into the same simple af algebra

on the classification of nuclear c algebras two of the most influential works on c algebras from the mid seventies brown douglas and fillmore s 6 and elliott s 21 both contain uniqueness and existence results in the now standard sense which we shall outline below these papers served as keystones for two separate theories kk theory and the classification program which for many years parted ways with only moderate interaction but with this common origin in mind it is not surprising that recent years have seen a fruitful interaction which has been one of the main engines behind rapid progress in the classification program in the present paper we take this interaction even further combining a concept of quasidiagonality for representations and a new characterization of equivalence in the cuntz picture of kk theory we achieve a general uniqueness result and from the quasidiagonality notion we derive a corresponding general existence result by comparing well known realizations of the kk groups these results are then employed to obtain new classification results for certain classes of quasidiagonal c algebras introduced by h lin an important novel feature of these classes is that they are defined by a certain local approximation property rather than by an inductive limit construction we emphasize that our fundamental uniqueness result does not depend on the universal coefficient theorem uct nor on nuclearity of the c algebras involved on the other hand when we refine the uniqueness result for use in classification we need to gradually add such conditions on the c algebras it is to be expected that requirements of this type are necessary but we have found that holding them back as long as possible leads to more conceptual proofs while clarifying the role of the uct and nuclearity in classification further since uniqueness results answer fundamental questions about kk and k theory they are of interest in themselves we have pursued this theme in 14 and defer to this paper the proof of the new characterization of kk theory which lies behind our uniqueness results our existence and uniqueness results are in the spirit of the classical ext theory from 6 the main complication overcome in the paper is to control the stabilization which is necessary when one works with finite c algebras in the infinite case where programs of this type have already been successfully carried out stabilization is unnecessary yet our methods are sufficiently versatile to allow us to reprove from a handful of basic results the classification of purely infinite nuclear c algebras of kirchberg and phillips

the stability of a cubic type functional equation with the fixed point alternative abstract in this note we investigate the generalized hyers ulam rassias stability for the new cubic type functional equation f x y 2 z f x y 2 z f 2 x f 2 y 2 f x y 2 f x z 2 f x z 2 f y z 2 f y z by using the fixed point alternative the first systematic study of fixed point theorems in nonlinear analysis is due to g isac and th m rassias internat j math math sci 19 1996 219 228

an optimization algorithm for clustering using weighted dissimilarity measures one of the main problems in cluster analysis is the weighting of attributes so as to discover structures that may be present by using weighted dissimilarity measures for objects a new approach is developed which allows the use of the k means type paradigm to efficiently cluster large data sets the optimization algorithm is presented and the effectiveness of the algorithm is demonstrated with both synthetic and real data sets

hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation this is applied to investigate homomorphisms between quasi banach algebras the concept of hyers ulam rassias stability originated from th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

fuzzy normed space of operators and its completeness in this paper the new definition of the fuzzy norm of a linear operator from one fuzzy normed linear space into another is introduced and the boundedness of such an operator is described furthermore the space of all bounded linear operators endowed with this fuzzy norm is studied consequently its topological structure as well as completeness is given and that it can itself be made into a fuzzy normed linear space is also shown

isomorphisms between unital c algebras abstract it is shown that every almost linear bijection h a b of a unital c algebra a onto a unital c algebra b is a c algebra isomorphism when h 2 n u y h 2 n u h y for all unitaries u a all y a and n 0 1 2 and that almost linear continuous bijection h a b of a unital c algebra a of real rank zero onto a unital c algebra b is a c algebra isomorphism when h 2 n u y h 2 n u h y for all u v a v v v 1 v is invertible all y a and n 0 1 2 assume that x and y are left normed modules over a unital c algebra a it is shown that every surjective isometry t x y satisfying t 0 0 and t u x u t x for all x x and all unitaries u a is an a linear isomorphism this is applied to investigate c algebra isomorphisms between unital c algebras

a separable brown douglas fillmore theorem and weak stability we give a separable brown douglas fillmore theorem let a be a separable amenable c algebra which satisfies the approximate uct b be a unital separable amenable purely infinite simple c algebra and h 1 h 2 a b be two monomorphisms we show that h 1 and h 2 are approximately unitarily equivalent if and only if h 1 h 2 in kl a b we prove that for any e 0 and any finite subset f a there exist 0 and a finite subset g a satisfying the following for any amenable purely infinite simple c algebra b and for any contractive positive linear map l a b such that l ab l a l b 0 there is 0 such that in any unital amenable purely infinite simple c algebra b if uv e i vu for a pair of unitaries then there exists a pair of unitaries u 1 and v 1 in b such that u 1 v 1 e i v 1 u 1 u 1 u e and v 1 v e

asymptotic aspect of the quadratic functional equation in multi normed spaces abstract we investigate the hyers ulam stability of the quadratic functional equation for mappings from abelian groups into multi normed spaces we also study the stability on a restricted domain and present an asymptotic behavior of the quadratic equation in the framework of multi normed spaces

on the stability of an n dimensional cubic functional equation abstract let n 2 be an integer number in this paper we investigate the generalized hyers ulam rassias stability in banach spaces and also banach modules over a banach algebra and a c algebra and the stability using the alternative fixed point of an n dimensional cubic functional equation in banach spaces f j 1 n 1 x j 2 x n f j 1 n 1 x j 2 x n j 1 n 1 f 2 x j 2 f j 1 n 1 x j 4 j 1 n 1 f x j x n f x j x n

approximate homomorphisms on jb triples abstract it is shown that for an approximate homomorphism f j b of a jb triple j into a jb triple b there exists a unique homomorphism h j b near the approximate homomorphism