and Applied Analysis 3 Theorem 1.3 see 26–28 . Let X, d be a complete generalized metric space and let J : X → X be a strictly contractive mapping with Lipschitz constant L < 1. Then for each given element x ∈ X, either d ( Jx, J 1x ) ∞ 1.7 for all nonnegative integers n or there exists a positive integer n0 such that 1 d Jx, J 1x < ∞, for all n ≥ n0; 2 the sequence {Jnx} converges to a fixed p...

We investigate the following generalized Cauchy functional equation f(αx+ βy) = αf(x) + βf(y) where α, β ∈ R \ {0}, and use a fixed point method to prove its generalized Hyers–Ulam–Rassias stability in Banach modules over a C∗-algebra.

Abstract In this paper, we introduce a new integral transform, namely Aboodh and apply the transform to investigate Hyers–Ulam stability, Hyers–Ulam–Rassias Mittag-Leffler–Hyers–Ulam Mittag-Leffler–Hyers–Ulam–Rassias stability of second order linear differential equations.

We prove a general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces, which is then used to obtain stability properties for different kinds of functional equations linear functional equations, generalized equation of the square root, spiral generalized gamma equations in random normed spaces. As direct and natural consequences of our results, we obtain general...

By using a fixed point method, we establish the Hyers–Ulam stability and the Hyers–Ulam–Rassias stability for a general class of nonlinear Volterra integral equations in Banach spaces. 2000 Mathematics Subject Classification: Primary 45N05, 47J05, 47N20, 47J99, Secondary 47H99, 45D05, 47H10.

The fixed point alternative methods are implemented to give generalized Hyers-Ulam-Rassias stability for the Pexiderized quadratic functional equation in the fuzzy version. This method introduces a metrical context and shows that the stability is related to some fixed point of a suitable operator.

We obtain the Hyers-Ulam stability and modified Hyers-Ulam stability for the equations of the formg(x+p)=φ(x)g(x) in the following settings: |g(x+p)−φ(x)g(x)| ≤ δ, |g(x+p)−φ(x)g(x)| ≤φ(x), |(g(x+p)/φ(x)g(x))−1| ≤ψ(x). As a consequence we obtain the stability theorems for the gamma functional equation.

Using the fixed point method, we prove the Hyers–Ulam stability of the Cauchy–Jensen functional equation and of the Cauchy–Jensen functional inequality in fuzzy Banach ∗-algebras and in induced fuzzy C-algebras. Furthermore, using the fixed point method, we prove the Hyers–Ulam stability of fuzzy ∗-derivations in fuzzy Banach ∗-algebras and in induced fuzzy C-algebras. Published by Elsevier Ltd

The question concerning the stability of group homomorphisms was posed by Ulam 1 . Hyers 2 solved the case of approximately additive mappings on Banach spaces. Aoki 3 provided a generalization of the Hyers’ theorem for additive mappings. In 4 , Rassias generalized the result of Hyers for linear mappings by allowing the Cauchy difference to be unbounded see also 5 . The result of Rassias has bee...

In this article, we introduce the multi-$m$-Jensen mappings and characterize them as a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability for such mappings. As a consequence, we show that every multi-$m$-Jensen mappings (under some conditions) is hyperstable.