Stability of Functional Equations in Multi-Banach Spaces via Fixed Point Approach

Abstract

In this paper, using the fixed point approach, we proved the Hyers-Ulam-Rassias stability of a Jensen-type quadratic functionalin Multi-Banach Spaces using the ideas from Dales and Polyakov [4].

Ulam Stability of new type additive functional equation in Multi-Banach Spaces

“…Rassias theorem was obtained by P.Gavruta [4]. Then, the stability problem of several functional equations has been extensively investigated by a many number of authors, and there are many interesting results concerning this problem ( [3,5,6,8,16,9,10,11,12,15]). Motivated by the above discussions, we prove the general solution of a new type additive functional equation…”

Hyers-Ulam-Rassias Stability of Functional Equations in Multi Banach Spaces

“…Moslehian et al [8] demonstrated the asymptotic aspects of the quadratic functional equations in multi-normed spaces. Further, for a detailed analysis of stability of functional equations in multi-normed spaces one may also refer to [6,7,10,11]. The functional equation Section 2, contains basic definitions and concepts that will be used in the further sections of paper.…”