We investigate the stability of Pexiderized mappings in Banach modules over a unital Banach algebra. As a consequence, we establish the Hyers–Ulam stability of the orthogonal Cauchy functional equation of Pexider type f 1 (x + y) = f 2 (x) + f 3 (y), x ⊥ y in which ⊥ is the orthogonality in the sense of Rätz.

In this paper, we define multi-normed spaces, and investigate some properties of multi-bounded mappings on multi-normed spaces. Moreover, we prove a generalized Hyers– Ulam–Rassias stability theorem associated to the Cauchy additive equation for mappings from linear spaces into multi-normed spaces.

Using the integrating factor method, this paper deals with the Hyers-Ulam stability of a class of exact differential equations of second order. As a direct application of the main result, we also obtain the HyersUlam stability of a special class of Cauchy-Euler equations of second order. c ©2016 All rights reserved.

The generalized Hyers–Ulam–Rassias stability of adjointable mappings on Hilbert C∗-modules are investigated. As a result, we get a solution for stability of the equation f(x)∗y = xg(y)∗ in the context of C∗-algebras. ∗2000 Mathematics Subject Classification. Primary 39B82, secondary 46L08, 47B48, 39B52 46L05, 16Wxx.

In this paper, the nonlinear stability of a functional equation in the setting of non-Archimedean normed spaces is proved. Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the and the theory of functional equations are also presented Key word: Hyers Ulam Rassias stability • cubic mappings • generalized normed space • Banach spac...

The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation

The generalized Hyers–Ulam–Rassias stability of adjointable mappings on Hilbert C∗-modules is investigated. As a corollary, we establish the stability of the equation f(x)∗y = xg(y)∗ in the context of C∗-algebras. We also prove that each approximately adjointable mapping is indeed adjointable.

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

In this paper, we consider a Hammerstein integral equation (Hammerstein IE) in two variables with of time delays. The aim paper is to investigate the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) considered IE via Banach’s fixed point theorem (Banach’s FPT) Bielecki metric. proofs new outcomes are based on these basic tools. As contributions present study, here, for first time, develop...

Through literature retrieval and classification, it can be found that for the fractional delay impulse differential system, existence uniqueness of solution UHR stability system are rarely studied by using polynomial function matrix. In this paper, we firstly introduce a new concept impulsive delayed Mittag–Leffler type vector function, which helps us to construct representation an exact linear...