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

on the hyers ulam rassias stability of approximately additive mappings abstract in this paper using an idea from the paper of p gvruta j math anal appl 184 1994 431 436 the results of th m rassias j math anal appl 158 1991 106 113 shall be generalized

stability for quadratic functional equation in the spaces of generalized functions in this paper we consider the general solution of quadratic functional equation f ax y f ax y f x y f x y 2 a2 1 f x for any integer a with a 1 0 1 moreover we reformulate and prove the hyers ulam rassias stability theorem of the above equation in the spaces of tempered distributions and fourier hyperfunctions the generalized hyers ulam stability originated from the 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

some further generalizations of the hyers ulam rassias stability of functional equations abstract in this paper we study the hyers ulam rassias stability theory by considering the cases where the approximate remainder is defined by f x y f x f y x y x y g 1 f x y g x h y x y x y g 2 2f x y 1 2 f x f y x y x y g 3 where g is a certain kind of algebraic system e is a real or complex hausdorff topological vector space and f g h are mappings from g into e we prove theorems for the hyers ulam rassias stability of the above three kinds of functional equations and obtain the corresponding error formulas

on the stability of functional equations on a square symmetric groupoid abstract let x be a square symmetric groupoid and y d a complete metric divisible square symmetric groupoid in this paper we obtain the hyers ulam stability problem of the functional inequality d g x y g x g y e x y for approximate mapping g x y of the functional equation f x y f x f y differing by e x 2 0 in particular we have investigated the case of f x f y h f x 1 t f y 1 t on some set y

a generalization of the darcy forchheimer equation involving an implicit pressure dependent relation between the drag force and the velocity abstract we study mathematical properties of steady flows described by the system of equations generalizing the classical porous media models of darcy and forchheimer the considered generalizations are outlined by implicit relations between the drag force and the velocity that are in addition parametrized by the pressure we analyze such drag force velocity relations which are described through a maximal monotone graph varying continuously with the pressure large data existence of a solution to this system is established whereupon we show that under certain assumptions on data the pressure satisfies a maximum or minimum principle even if the drag coefficient depends on the pressure exponentially

unsteady flows of fluids with pressure dependent viscosity in this short paper we consider the unsteady flows of fluids with pressure dependent viscosities when the effect of gravity has to be taken into account such a situation presents itself in many technologically relevant flows after developing the appropriate governing equations we establish qualitative results concerning the nature of the solutions to the governing equations as well as uniqueness results we then obtain explicit exact solutions for two initial boundary value problems namely modified stokes first and second problems such explicit solutions serve a dual purpose they present exact results for idealized problems that reflect practical situations and they provide a means for checking the numerical schemes that are developed for flows in more complex situations

addendum to on the stability of functional equations on square symmetric groupoid abstract let x be a square symmetric groupoid and y d a complete metric divisible square symmetric groupoid in this paper we obtain the hyers ulam stability problem of functional inequality d g x y g x g y e x y for approximate mapping g x y of functional equation f x y f x f y differing by e x 2 0 in particular we have investigated the case of f x f y h f x 1 t f y 1 t on some set y

breather solutions for inhomogeneous fpu models using birkhoff normal forms abstract we present results on spatially localized oscillations in some inhomogeneous nonlinear lattices of fermi pasta ulam fpu type derived from phenomenological nonlinear elastic network models proposed to study localized protein vibrations the main feature of the fpu lattices we consider is that the number of interacting neighbors varies from site to site and we see numerically that this spatial inhomogeneity leads to spatially localized normal modes in the linearized problem this property is seen in 1 d models and in a 3 d model with a geometry obtained from protein data the spectral analysis of these examples suggests some non resonance assumptions that we use to show the existence of invariant subspaces of spatially localized solutions in quartic birkhoff normal forms of the fpu systems the invariant subspaces have an additional symmetry and this fact allows us to compute periodic orbits of the quartic normal form in a relatively simple way

on the general solution and hyperstability of the general radical quintic functional equation in quasi β banach spaces abstract the goal of this paper is to study the general solution of the following general radical quintic functional equation f a x 5 b y 5 5 r f x s f y for f a mapping from the field of real numbers into a vector space where a b r s are fixed nonzero reals also we prove the generalized hyperstability results for the general radical quintic functional equation by using the fixed point theorem cf dung and hang 2018 15 theorem 2 1 in quasi banach spaces namely we show under some weak natural assumptions functions satisfying the above equation approximately in some sense must be actually solutions to it

instabilities of breathers in a finite nls lattice abstract we study some aspects of the dynamics of unstable breathers in a three site discrete cubic nls chain with dirichlet boundary conditions we view breathers as fixed points of the energy in the reduced phase space obtained by eliminating directions related to the global phase symmetry of the system we use a combination of numerical calculations and morse theoretical arguments to see that there are two breathers that correspond to critical energies where the energy hypersurface changes its connectivity these breathers are elliptic hyperbolic fixed points of the reduced four dimensional system we compute the periodic orbits in their center manifolds lyapunov orbits and see evidence for homoclinic intersections of their stable and unstable manifolds we also examine the possibility of heteroclinic connections between lyapunov orbits these however appear not to exist for the energies near the energy where the energy hypersurface becomes connected

squeeze flow of a piezoviscous fluid we investigate squeeze flow of piezoviscous fluids presence of contact line leads to strong pressure variations strong pressure variations induce strong viscosity variations in piezoviscous fluid squeeze flow characteristics are influenced by piezoviscosity of the fluid we investigate the squeeze flow of a piezoviscous fluid the classical navier stokes fluid model and the no slip boundary condition on the plate fluid interface implies the presence of the pressure singularity at the contact line it can be conjectured that the same behaviour is present even for piezoviscous fluids consequently the pressure variation in the fluid could be large and the pressure dependent viscosity could be important even if the piezoviscous coefficient is apparently small we investigate this conjecture by means of numerical simulation based on a variant of the spectral collocation method the numerical simulations indicate that the effects due to pressure dependent viscosity are for certain range of parameter values significant

a distributional version of functional equations and their stabilities abstract generalizing the results in j math anal appl 286 2003 177 186 j math anal appl 295 2004 107 114 arch math to appear j math anal appl 299 2004 578 586 that consider the hyers ulam stability problems of several functional equations in the spaces of the schwartz tempered distributions and the fourier hyperfunctions we consider the stability problems of the functional equations in the space of distributions

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

a generalization of the hyers ulam rassias stability of the pexiderized quadratic equations abstract in this paper we prove the hyers ulam rassias stability by considering the cases that the approximate remainder is defined by f x y f x y 1 2g x 2g y x y f x y g x y 1 2h x 2k y x y where g is a group x is a real or complex hausdorff topological vector space and f g h k are functions from g into x

on the hyers ulam stability of the functional equations that have the quadratic property abstract the hyers ulam stability of the quadratic functional equation 1 on a restricted domain shall be investigated and the result shall be applied to the study of an asymptotic behavior of that equation furthermore the hyers ulam stability problems of another quadratic equation 4 on a restricted domain shall also be treated under the approximately even or odd condition and some asymptotic behaviors of the quadratic mappings and the additive mappings shall be investigated

stability of functional equations on restricted domains in a group and their asymptotic behaviors in this paper we consider hyers ulam stability problems for the pexider equation the cauchy equation and the jensen equation in general restricted domains in a group the main purpose of this paper is to find restricted domains such that the functional inequality satisfied in those domains extends to the inequality for the whole domain and such that the hyers ulam stability theorem holds for the inequalities as it does when the inequality holds globally we also consider a distributional version of the hyers ulam stability of the pexider equation in restricted domains and its asymptotic behaviors

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

a fixed point method for perturbation of bimultipliers and jordan bimultipliers in c ternary algebras let a be a c ternary algebra a c bilinear t a a a is called a c ternary algebra bi multiplier if it satisfies t abc d t a b cd t a bcd abt c d for all a b c d a also the mapping t a a a is a called c ternary algebra jordan bimultiplier if it satisfies t aaa a t a a aa t a aaa aat a a for all a a using the fixed point method we investigate the generalized hyers ulam rassias stability of bimultipliers and jordan bimultipliers in c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias proc am math soc 72 297 1978

stability of functional equations of drygas in the space of schwartz distributions in this paper we reformulate and prove the stability theorems of s m jung and p k sahoo s m jung p k sahoo stability of a functional equation of drygas aequationes math 64 2002 263 273 in the spaces of generalized functions such as the schwartz distributions and tempered distributions

on a generalized nonlinear functional equation abstract the paper deals with the functional equation f x f f u x f v x under some special assumptions concerning the given functions u v and f our main result extends some results in the literature

hyers ulam rassias stability of a linear recurrence abstract in this paper we give a hyers ulam rassias stability result for the first order linear recurrence in banach spaces

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

vector valued invariant means revisited abstract we show that a banach space x is complemented in its ultraproducts if and only if for every amenable semigroup s the space of bounded x valued functions defined on s admits a an invariant average or b what we shall call an admissible assignment condition b still provides an equivalence for quasi banach spaces while condition a necessarily implies that the space is locally convex

a new type of approximation for the radical quintic functional equation in non archimedean 2 β banach spaces abstract let r be the set of real numbers in this paper we first introduce the notions of non archimedean 2 normed spaces x and we will reformulate the fixed point theorem 10 theorem 1 in this space after it we introduce and solve the radical quintic functional equation f x 5 y 5 5 f x f y x y r also under some weak natural assumptions on the function r r x 0 we show that this theorem is a very efficient and convenient tool for proving the hyperstability results when f r x satisfy the following radical quintic inequality f x 5 y 5 5 f x f y z x y z x y r 0 z x with x y

stability of exponential equations in schwartz distributions abstract we reformulate the superstability of exponential equation and cosine functional equation j a baker the stability of cosine equation proc amer math soc 80 1980 411 416 in some spaces of generalized functions such as the schwartz distributions sato hyperfunctions and gelfand generalized functions which completes the previous results of partial generalizations of the stability problems j chung a distributional version of functional equations and their stabilities nonlinear anal 62 2005 1037 1051 j chung s y chung d kim the stability of cauchy equations in the space of schwartz distributions j math anal appl 295 2004 107 114

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

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

the space of psi gamma additive mappings on semigroups in this paper we introduce the concept of pseudoadditive mappings from a semigroup into a banach space and we provide a generalized solution of ulam s problem for approximately additive mappings

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

low dimensional q tori in fpu lattices dynamics and localization properties abstract recent studies on the fermi pasta ulam fpu paradox like the theory of q breathers and the metastability scenario dealing mostly with the energy localization properties in the fpu space of normal modes q space motivated our first work on q tori in the fpu problem christodoulidi et al 2010 19 the q tori are low dimensional invariant tori hosting trajectories that present features relevant to the interpretation of fpu recurrences as well as the energy localization in q space the present paper is a continuation of our work in christodoulidi et al 2010 19 our new results are we extend a method of analytical computation of q tori using poincare lindstedt series from the to the fpu and we reach significantly higher expansion orders using an improved computer algebraic program we probe numerically the convergence properties as well as the level of precision of our computed series we develop an additional algorithm in order to systematically locate values of the incommensurable frequencies used as an input in the pl series construction of q tori corresponding to progressively higher values of the energy we generalize a proposition proved in christodoulidi et al 2010 19 regarding the so called sequence of propagation of an initial excitation in the pl series we show by concrete examples how the latter interprets the localization patterns found in numerical simulations we focus in particular on various types of extensive initial excitations that lead to q tori solutions with exponentially localized profiles finally we discuss the relation between q tori q breathers viewed as one dimensional q tori and the so called fpu trajectories invoked in the original study of the fpu problem

stability of c inner products abstract in this paper we investigate the stability of the inner products in hilbert c modules over unital c algebras

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

a generalization of the hyers ulam rassias stability of the pexider equation in this paper we prove a generalization of the stability of the pexider equation f x y g x h y in the spirit of hyers ulam rassias and g vruta

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

isomorphisms between c ternary algebras in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following generalized cauchy jensen additive mapping 2f j 1pxj2 j 1dyj j 1pf xj 2 j 1df yj this is applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the rassias stability theorem that appeared in his paper on the stability of the linear mapping in banach spaces see proc amr math soc 72 297 300 1978

on metastability in fpu we present an analytical study of the fermi pasta ulam fpu model with periodic boundary conditions we analyze the dynamics corresponding to initial data with one low frequency fourier mode excited we show that correspondingly a pair of kdv equations constitute the resonant normal form of the system we also use such a normal form in order to prove the existence of a metastability phenomenon more precisely we show that the time average of the modal energy spectrum rapidly attains a well defined distribution corresponding to a packet of low frequencies modes subsequently the distribution remains unchanged up to the time scales of validity of our approximation the phenomenon is controlled by the specific energy

on the stability of euler lagrange type cubic mappings in quasi banach spaces abstract in this paper we solve the generalized hyers ulam rassias stability problem for euler lagrange type cubic functional equations f a x y f x a y a 1 a 1 2 f x f y a a 1 f x y for mappings f x y in quasi banach spaces and for fixed integers a with a 0 1 in addition we also present a counterexample that does not satisfy the stability based on ulam s question

stability problem of ulam for generalized forms of cauchy functional equation abstract let g 1 be a vector space and g 2 a banach space in this paper we solve the generalized hyers ulam rassias stability problem for a generalized form g i 1 n a i x i c i 1 n a i g x i c x i g 1 of cauchy functional equation f x y f x f y for a mapping f g 1 g 2 where a i a i are scalars for all i 1 n and c g 1 c g 2 are vectors

on steady flows of fluids with pressure and shear dependent viscosities there are many technologically important problems such as elastohydrodynamics which involve the flows of a fluid over a wide range of pressures while the density of the fluid remains essentially constant during these flows whereby the fluid can be approximated as being incompressible the viscosity varies significantly by several orders of magnitude it is also possible that the viscosity of such fluids depends on the shear rate here we consider the flows of a class of incompressible fluids with viscosity that depends on the pressure and shear rate we establish the existence of weak solutions for the steady flows of such fluids subjected to homogeneous dirichlet boundary conditions and to specific body forces that are not necessarily assumed to be small a novel aspect of the study is the manner in which we treat the pressure that allows us to establish its compactness as well as that of the velocity gradient the method draws upon the physics of the problem namely that the notion of incompressibility is an idealization that is attained by letting the compressibility of the fluid to tend to zero

energy localization on q tori long term stability and the interpretation of fermi pasta ulam recurrences we focus on two approaches that have been proposed in recent years for the explanation of the so called fermi pasta ulam fpu paradox i e the persistence of energy localization in the low q fourier modes of fermi pasta ulam nonlinear lattices preventing equipartition among all modes at low energies in the first approach a low frequency fraction of the spectrum is initially excited leading to the formation of natural packets exhibiting exponential stability while in the second emphasis is placed on the existence of q breathers i e periodic continuations of the linear modes of the lattice which are exponentially localized in fourier space following ideas of the latter we introduce in this paper the concept of q tori representing exponentially localized solutions on low dimensional tori and use their stability properties to reconcile these two approaches and provide a more complete explanation of the fpu paradox

spectra of chains connected to complete graphs abstract we characterize the spectrum of the laplacian of graphs composed of one or two finite or infinite chains connected to a complete graph we show the existence of localized eigenvectors of two types eigenvectors that vanish exactly outside the complete graph and eigenvectors that decrease exponentially outside the complete graph our results also imply gaps between the eigenvalues corresponding to localized and extended eigenvectors

ulam stability problem for quadratic mappings of euler lagrange abstract the purpose of this paper is to solve the stability problem of ulam for an approximate mapping f a b of the following quadratic functional equation of euler lagrange a b aq x a b bq y q ax by abq x y for all x y a with a and b linear spaces

on the hyers ulam rassias stability of an additive functional equation in quasi banach spaces abstract in this paper we investigate the hyers ulam rassias stability of the following functional equation i 1 m f m x i j 1 j i m x j f i 1 m x i 2 f i 1 m m x i m n m 2 in quasi banach spaces

on the hyers ulam rassias stability of functional equations in n variables abstract in this paper we investigate a generalization of the hyers ulam rassias stability for a functional equation of the form f x x f x x and the stability in the sense of ger for the functional equation of the form f x x f x where x lie in n variables as a consequence we obtain a stability result in the sense of hyers ulam rassias g vruta and ger for some well known equations such as the gamma beta and g function type s equations

global analysis of the flows of fluids with pressure dependent viscosities to describe the flows of fluids over a wide range of pressures it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure that the viscosity depends on the pressure has been verified by numerous careful experiments while the existence of solutions local in time to the equations governing the flows of such fluids are available for small special data and rather unrealistic dependence of the viscosity on the pressure no global existence results are in place our interest here is to establish the existence of weak solutions for spatially periodic three dimensional flows that are global in time for a large class of physically meaningful viscosity pressure relationships

isomorphisms between c ternary algebras abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following cauchy jensen additive mappings 0 1 f x y 2 z f x y 2 z f x 2 f z 0 2 f x y 2 z f x y 2 z f y 0 3 2 f x y 2 z f x f y 2 f z these are applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the 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 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

on the stability problem for a mixed type of quartic and quadratic functional equation let e1 and e2 be real linear spaces in this paper we determine the general solution for a mixed type functional equation of a quartic and a quadratic mapping f e1 e2 x2 xnn 1f x1 2n 1 n 2 i 1nf xi 2n 2 1 i j n xjf xi for all n variables x1 xn e1 where n 2 in addition we solve the generalized hyers ulam rassias stability problem for the functional equation

stability of a quadratic jensen type functional equation in the spaces of generalized functions abstract making use of the fundamental solution of the heat equation we find the solution and prove the stability theorem of the quadratic jensen type functional equation 9 f x y z 3 f x f y f z 4 f x y 2 f y z 2 f z x 2 in the spaces of schwartz tempered distributions and fourier hyperfunctions

conditional functional equations on restricted domains of measure zero let r02 r2 0 0 r 2 x y r2 x2 y2 and f r02 r g r 2 r in this paper we consider the ulam hyers stability of the functional equations f ux vy uy vx f x y f u v f ux vy uy vx f x y f u v g ux vy uy vx g x y g u v g ux vy uy vx g x y g u v for all x y u v where r4 is of 4 dimensional lebesgue measure zero the above functional equations are modified versions of the equations in 9 11 14 18 24 which arise from number theory and are in connection with characterizations of determinant and permanent of two by two matrices

on the generalized hyers ulam stability of module left derivations let a be a unital normed algebra and let m be a unitary banach left a module if f a m is an approximate module left derivation then f a m is a module left derivation moreover if m a is a semiprime unital banach algebra and f tx is continuous in t r for each fixed x in a then every approximately linear left derivation f a a is a linear derivation which maps a into the intersection of its center z a and its jacobson radical rad a in particular if a is semisimple then f is identically zero

on approximation of approximately linear mappings by linear mappings abstract assume a is a normed linear space b is a banach space and f a b is a mapping approximately linear we solve the following ulam problem give conditions in order for a linear mapping near an approximately linear mapping to exist

computation of periodic solution bifurcations in odes using bordered systems we consider numerical methods for the computation and continuation of the three generic secondary periodic solution bifurcations in autonomous odes namely the fold the period doubling or flip bifurcation and the torus or neimark sacker bifurcation in the fold and flip cases we append one scalar equation to the standard periodic bvp that defines the periodic solution in the torus case four scalar equations are appended evaluation of these scalar equations and their derivatives requires the solution of linear bvps whose sparsity structure after discretization is identical to that of the linearization of the periodic bvp therefore the calculations can be done using existing numerical linear algebra techniques such as those implemented in the software auto and colsys

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

the stability of cauchy s gamma beta functional equation abstract we obtain the super stability of cauchy s gamma beta functional equation b x y f x y f x f y where b x y is the beta function and investigate the stability in the sense of r ger of this equation in the following setting b x y f x y f x f y 1

a note on ulam stability of some fuzzy number valued functional equations abstract this note investigates the ulam stability of the following fuzzy number valued functional equations in banach spaces by using the metric defined on a fuzzy number space f x y 2 f x y 2 f x and f a x b y r f x s f y

hyers ulam rassias stability of an equation of davison abstract in this work the hyers ulam rassias stability of the davison functional equation f xy f x y f xy x f y is proved

approximate solution of radical quartic functional equation related to additive mapping in 2 banach spaces abstract the aim of this paper is first to reformulate the fixed point theorem 4 theorem 1 in 2 banach spaces after it we introduce and solve the radical quartic functional equation f x 4 y 4 4 f x f y we also show that the fixed point methods allow to investigate ulam s type stability of radical quartic functional equation in 2 banach spaces