Almost Generalized Quadratic Functions of Three Variables in Lipschitz Spaces

Abstract

The notion of stability of functional equations was posed by Ulam, and then, Hyers gave the first significant partial solution. This type of stability has been established and developed by an increasing number of mathematicians in various spaces. In Lipschitz spaces, the notion of stability was introduced by Tabor and Czerwik. This notion has been considered less attention over the recent years in Lipschitz spaces. In this paper, we consider this type of stability and we prove the stability of the generalized quadratic functional equations of three variables in Lipschitz spaces. We generalize the stability of a quadratic functional equation from a special case to a general case and improve its approximation announced by Czerwik et al. in [4].

Key words and phrases. Stability, Lipschitz space, Quadratic functional equation.

2010 Mathematics Subject Classification. 39B82, 47A60, 39B52