Generalized Stability of Euler‐Lagrange Quadratic Functional Equation

Abstract

The main goal of this paper is the investigation of the general solution and the generalized Hyers-Ulam stability theorem of the following Euler-Lagrange type quadratic functional equationf(ax+by)+af(x-by)=(a+1)b2f(y)+a(a+1)f(x), in(β,p)-Banach space, wherea,bare fixed rational numbers such thata≠-1,0andb≠0.

Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN Spaces

“…The paper [20] also demonstrated that this kind of cubic functional equation is Hyers-Ulam-Rassias stable. Numerous mathematicians have studied several Euler-Lagrange-type functional equations (for example, [21][22][23][24][25][26][27][28][29]).…”

Approximate Euler-Lagrange Quadratic Mappings in Fuzzy Banach Spaces

“…in [8][9][10]. The stability problems of several functional equations have been extensively investigated by a number of authors, and there are many interesting results concerning this problem (see [11][12][13][14]). The theory of fuzzy space has much progressed as the theory of randomness has developed.…”

Solution and Stability of Euler-Lagrange-Rassias Quartic Functional Equations in Various Quasinormed Spaces

“…Several Euler-Lagrange type functional equations have been investigated by numerous mathematicians; c.f. for example, [13][14][15].…”