Generalized Hyers-Ulam-Rassias Stability of an Euler-Lagrange Type Cubic Functional Equation in Non-Archimedean Quasi-Banach Spaces.

In this study, we aim to prove the generalized Hyers-Ulam-Rassias (GHUR) stability for the following Euler-Lagrange (EL) type cubic functional equation f(bx+y)+f(x+by)=(b+1)(b-1)²[f(x)+f(y)]+b(b+1)f(x+y) in non-Archimedean (n.A) quasi-Banach spaces and n.A (n,β) Banach spaces. In recent decades, the stability of functional equations has emerged as one of the most intriguing and engaging topics, as it leads to the applications of functional equations in various domains such as algebraic geometry, Group theory, Mechanics etc., This study is to investigate the GHUR stability for the above equation using Hyers direct method. Furthermore, we obtain the stability results for the aforementioned equation with an illustrative example for the n.A case. With the study of the example one may easily understand how the stability result of functional equations in n.A case differs from the setting of classical Banach spaces. [ABSTRACT FROM AUTHOR]

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