In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...

In this paper we introduce a notion of a non-Archimedean fuzzy norm and study the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces in the spirit of Hyers–Ulam–Rassias–Găvruţa. As a corollary, the stability of the Jensen equation is established. We indeed present an interdisciplinary relation between the theory of fuzzy spaces, the theory of non-Archimedean spaces ...

Let X be a linear space over K∈{R,C}, Y real or complex Banach and f:Xn→Y. With some fixed aji,Ci1…in∈K (j∈{1,…,n}, i,ik∈{1,2}, k∈{1,…,n}), we study, using the direct point methods, stability general of equation f(a11x11+a12x12,…,an1xn1+an2xn2)=∑1≤i1,…,in≤2Ci1…inf(x1i1,…,xnin), for all xjij∈X (j∈{1,…,n},ij∈{1,2}). Our paper generalizes several known results, among others concerning equations wi...

Abstract We prove a very general fixed point theorem in the space of functions taking values random normed (RN-space). Next, we show several its consequences and, among others, present applications it proving Ulam stability results for inhomogeneous linear functional equation with variables class f mapping vector X into an RN-space. Particular cases are instance equations Cauchy, Jensen, Jordan...

In this paper, we investigate homomorphisms from unital C∗−algebras to unital Banach algebras and derivations from unital C∗−algebras to Banach A−modules related to a Cauchy–Jensen functional inequality. Mathematics subject classification (2010): 39B72, 46H30, 46B06.

Abstract. The study of dynamic equations on time scales, which goes back to its founder Stefan Hilger (1988), is an area of mathematics which is currently receiving considerable attention. Although the basic aim of this is to unify the study of differential and difference equations, it also extends these classical cases to “in between”. In this paper we present time scales versions of the inequ...