A new type of Hyers-Ulam-Rassias stability for Drygas functional equation
محورهای موضوعی : Functional analysisM. 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
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].
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