distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we investigate the generalized Hyers-Ulam stability of a functional equation 1≤i,j≤n, i =j f (x i + x j) + f (x i − x j) = (n − 1) n i=1 3f (x i) + f (−x i) .

in this paper, we obtain the general solution and the generalized  hyers--ulam--rassias stability in random normed spaces, in non-archimedean spacesand also in $p$-banach spaces and finally the stability viafixed point method for a functional equationbegin{align*}&d_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1...

‎In 1897‎, ‎Hensel introduced a normed space which does‎ ‎not have the Archimedean property‎. ‎During the last three decades‎ ‎theory of non--Archimedean spaces has gained the interest of‎ ‎physicists for their research in particular in problems coming‎ ‎from quantum physics‎, ‎p--adic strings and superstrings‎. ‎In this paper‎, ‎we prove‎ ‎the generalized Hyers--Ulam--Rassias stability for a‎ ...

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea Full list of author information is available at the end of the article Abstract In this article, we prove the Hyers-Ulam stability of exact second-order linear differential equations. As a consequence, we show the Hyers-Ulam stability of the fo...

In this paper, the authors investigate the generalized Ulam-Hyers stability of a Leibniz type additive and quadratic functional equation ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + + − + − + − 3 2 3 3 = ) ( ) ( ) ( z y x f t z y x f t z f t y f t x f ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + − + 3 2 3 2 z y x f z y x f in the setting of intuitionistic fuzzy normed spaces using direct and fixed point methods.

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

Abstract This article discusses the stability results for solution of a fractional q -integro-differential problem via integral conditions. Utilizing Krasnoselskii’s, Banach fixed point theorems, we demonstrate existence and uniqueness results. Based on obtained, conditions are provided to ensure generalized Ulam Ulam–Hyers–Rassias stabilities original system. The illustrated by two examples.

In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class higher integro-differential equations. particular, consider new kind stability, the σ-semi-Hyers-Ulam which is some sense between Hyers–Ulam and Hyers–Ulam–Rassias stabilities. These result from application Banach Fixed Point Theorem, by applying specific generalization Bielecki ...

Keywords---Hyers-Ulam-Rassias stability, Functional equation, Riemann zeta function, Square root spital. 1. I N T R O D U C T I O N The staxting point of studying the stability of functional equations seems to be the famous talk of Ulam [2] in 1940, in which he discussed a number of important unsolved problems. Among those was the question concerning the stability of group homomorphisms. Let G1...

* Correspondence: [email protected]. kr Department of Mathematics, Daejin University, Kyeonggi 487711, Korea Full list of author information is available at the end of the article Abstract Using fixed point method, we investigate the Hyers-Ulam stability and the superstability of partial generalized Jordan derivations on Banach modules related to Jensen type functional equations. Mathematics Subj...