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

محورهای موضوعی : Functional analysis

M. Sirouni ¹ , M. ‎Almahalebi ² , S. ‎Kabbaj ³

1 - Department of Mathematics, Faculty of Science, Ibn Tofail University, BP-14000, Kenitra, Morocco
2 - Department of Mathematics, Faculty of Science, Ibn Tofail University, BP-14000, Kenitra, Morocco
3 - Department of Mathematics, Faculty of Science, Ibn Tofail University, BP-14000, Kenitra, Morocco

تاریخ دریافت : 1396/10/05 تاریخ پذیرش : 1397/04/05 تاریخ انتشار : 1397/08/10

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

چکیده مقاله :

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].