A new type of Hyers-Ulam-Rassias stability for Drygas functional equation

Subject Areas : Functional analysis

M.  Sirouni ¹ (Department of Mathematics, Faculty of Science, Ibn Tofail University, BP-14000, Kenitra, Morocco)
M.  ‎Almahalebi ² (Department of Mathematics, Faculty of Science, Ibn Tofail University, BP-14000, Kenitra, Morocco)
S.  ‎Kabbaj ³ (Department of Mathematics, Faculty of Science, Ibn Tofail University, BP-14000, Kenitra, Morocco)

Received: 2017-12-26 Accepted : 2018-06-26 Published : 2018-11-01

Keywords: Stability, fixed point method, Banach space, hyperstability, Drygas functional equation,

Abstract :

In this paper, we prove the generalized Hyers-Ulam-Rassias stability for the Drygas functional equation$$f(x+y)+f(x-y)=2f(x)+f(y)+f(-y)$$ in Banach spaces by using the Brz\c{d}ek's fixed point theorem. Moreover, we give a general result on the hyperstability of this equation. Our results are improvements and generalizations of the main result of M. Piszczek and J. Szczawi\'{n}ska [21].

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