In this paper, we introduce the following additive type functional equation f(rx+ sy) = r + s 2 f(x+ y) + r − s 2 f(x− y), where r, s ∈ R with r + s, r − s 6= 0. Also we investigate the Hyers–Ulam–Rassias stability of this functional equation in Banach modules over a unital C∗-algebra. These results are applied to investigate homomorphisms between C∗-algebras. 2000 Mathematics Subject Classific...

Fractional calculus is nowadays an efficient tool in modelling many interesting nonlinear phenomena. This study investigates, a novel way, the Ulam–Hyers (HU) and Ulam–Hyers–Rassias (HUR) stability of differential equations with general conformable derivative (GCD). In our analysis, we employ some version Banach fixed-point theory (FPT). this generalize several earlier results. Two examples are...

We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism f from a Banach algebra into a semisimple commutative...

<abstract><p>We prove existence and uniqueness of solutions to discrete fractional equations that involve Riemann-Liouville Caputo derivatives with three-point boundary conditions. The results are obtained by conducting an analysis via the Banach principle Brouwer fixed point criterion. Moreover, we stability, including Hyers-Ulam Hyers-Ulam-Rassias type results. Finally, some numer...

In this work, by considering a class of matrix valued fuzzy controllers and using (?,?)-Cauchy–Jensen additive functional equation ((?,?)-CJAFE), we apply the Radu–Mihet method (RMM), which is derived from an alternative fixed point theorem, obtain existence unique solution H–U–R stability (Hyers–Ulam–Rassias) for homomorphisms Jordan on Lie algebras with ? members (?-LMVFA). With regards to ea...

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...

An elastic beam equation (EBEq) described by a fourth-order fractional difference is proposed in this work with three-point boundary conditions involving the Riemann–Liouville operator. New sufficient ensuring solutions’ existence and uniqueness of problem are established. The findings obtained employing properties discrete equations, Banach contraction, Brouwer fixed-point theorems. Further, w...

Abstract In this study, an initial-value problem for a nonlinear Volterra functional integro-differential equation on finite interval was considered. The term in the contains multiple time delays. addition to giving some new theorems existence and uniqueness of solutions equation, authors also prove Hyers-Ulam-Rassias stability Hyers-Ulam equation. proofs use several different tools including B...

In this paper, we prove the generalized Hyers–Ulam stability of a quadratic and quartic functional equation in intuitionistic fuzzy Banach spaces.