Perturbation of n dimensional AQ - mixed type functional equation via Banach spaces and Banach algebra : Hyers direct and alternative fixed point methods

Abstract

In this paper, the authors obtain the general solution and generalized Ulam -Hyers stability of n dimensional additive quadratic functional equationin Banach spaces using direct and fixed point methods. We also investigate the stability of the above equation in Banach algebra using direct and fixed point approach.

General solution and generalized Ulam-Hyers stability of a generalized n- type additive quadratic functional equation in Banach space and Banach algebra: direct and fixed point methods

“…Hence, the mapping : A X Y  is a unique Additive Derivation satisfying (135). This following corollary is a immediate consequence of Theorem 10.2 concerning the stability of (11…”

“…In this section, we discuss the generalized Ulam-Hyers stability of the functional equation (11) for the mixed case.…”

“…In this section, the general solution of the functional equation (11), for the odd case is discussed. Throughout this section, let us consider X and Y to be real vector spaces.…”

“…Over the last seven decades, the above problem was talked by numerous authors and its solutions via various forms of functional equations like, additive, quadratic, cubic, quartic mixed type functional equations were discussed. We refer the interested readers for more information on such problems to the monographs of [4], [6], [9], [11], and [13].…”

“…It follows from Theorem 7.1 that A is a unique additive mapping and satisfies(11) for all xX   be a odd mapping and there exists a real numbers  and s such that,…”