In this paper, the existence of solution and its stability to fractional boundary value problem (FBVP) were investigated for an implicit nonlinear differential equation (VOFDE) variable order. All criteria solutions in our establishments derived via Krasnoselskii’s fixed point theorem sequel, Ulam–Hyers–Rassias (U-H-R) is checked. An illustrative example presented at end paper validate findings.

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 ...

Abstract This article deals with the existence, uniqueness and Ulam-Hyers--Rassias stability results for a class of coupled systems implicit fractional differential equations Riesz-Caputo derivative boundary conditions. We will employ Banach’s contraction principle as well Schauder’s fixed point theorem to demonstrate our existence results. provide an example illustrate obtained

In the paper we establish the general solution of the function equation f(2x+y)+f(2x-y) = f(x+y)+f(x-y)+2f(2x)-2f(x) and investigate the Hyers-Ulam-Rassias stability of this equation in 2-Banach spaces.

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:begin{equation} sum_{ j = 1}^{n}fBig(-2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}Big) =(n-6) fBig(sum_{ i = 1}^{n} x_{i}Big) + 9 sum_{ i = 1}^{n}f(x_{i}).end{equation}

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

Copyright q 2010 Dongseung Kang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the generalized Hyers-Ulam-Rassias stability problem in quasi-β-normed spaces and then the stability by using a subadditive function f...

In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in proper CQ∗-algebras and of generalized derivations on proper CQ∗-algebras for the following Cauchy-Jensen additive mappings: f ( x + y + z 2 ) + f ( x− y + z 2 ) = f(x) + f(z), f ( x + y + z 2 ) − f ( x− y + z 2 ) = f(y), 2f ( x + y + z 2 ) = f(x) + f(y) + f(z), which were introduced and investigated in [3, 30]. This i...

Problem 1.1. Given a metric group (G,·,d), a positive number ε, and a mapping f : G→ G which satisfies the inequality d( f (xy), f (x) f (y)) ≤ ε for all x, y ∈ G, do there exist an automorphism a of G and a constant δ depending only on G such that d(a(x), f (x)) ≤ δ for all x ∈G? If the answer to this question is affirmative, we say that the equation a(xy) = a(x)a(y) is stable. A first answer ...