On Stability of Generalized Quadratic Functional Equation in 2-Banach Spaces
Bhavin Mansukhlal Patel *
Department of Mathematics, Gujarat Arts and Science College, Ahmedabad, Gujarat, India.
*Author to whom correspondence should be addressed.
Abstract
Stability of functional equations was initiated by Ulam (1960). The stability problem for functional equations have been
extensively investigated by a number of great mathematicians (Zenada and Elmaged, 2024; Alessa and Tamilvanan, 2021;
Tamilvanan et al., 2020). During the last five decades, lots of research articles and research monographs have been published on various generalizations and applications of the Hyers-Ulam stability for several functional equations. In this research article, we find the general solution of functional equation.
h(ba+c)+h(a−bc) = (b2+1)h(a)+(b2+1)h(c)
a,c ∈ X, b ∈ N and we prove the generalized Hyers-Ulam Stability of above functional equation in 2-Banach spaces.
Keywords: Generalized, quadratic functional equation, banach spaces, linear space