Cauchy-Jensen additive mappings in quasi-Banach algebras and its applications

In this paper, we prove the Hyers-Ulam stability of homomorphisms in quasi-Banach algebras and of generalized derivations on quasi-Banach algebras for the following Cauchy-Jensen additive mapping

GENERALIZED HYERS–ULAM STABILITY OF AN AQCQ-FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN BANACH SPACES

Abstract. In this paper, we prove the generalized Hyers–Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x + 2y) + f(x − 2y) = 4f(x + y) + 4f(x − y) − 6f(x) + f(2y) + f(−2y) − 4f(y) − 4f(−y) in non-Archimedean Banach spaces. 1. Introduction an

On Pexider Differences in Topological Vector Spaces

Let be a normed space and a sequentially complete Hausdorff topological vector space over the field ℚ of rational numbers. Let 1={(,)∈×∶‖‖+‖‖≥}, and 2={(,)∈×∶‖‖+‖‖0. We prove that the Pexiderized Jensen functional equation is stable for functions defined on 1(2), and taking values in . We consider also the Pexiderized Cauchy functional equation

GG-dual Frames in Hilbert C∗C^{*}-module Spaces

In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames  are given.  A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is not satisfied in general Hilbert $C^*$-modules

Homomorphisms and Derivations in C*-Algebras

Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms in C*-algebras, Lie C*-algebras, and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras, and JC*-algebras associated with the following Apollonius-type additive functional equation f(z−x)+f(z−y)+(1/2)f(x+y)=2f(z−(x+y)/4)