A fixed point method for the stability of functional equations in probabilistic normed quasi-linear spaces

Abstract

In this article, we define probabilistic normed quasi-linear spaces and provide some introductions and examples to clarify the structure of these spaces. We then investigate the generalized Hyers-Ulam stability of the (additive) Cauchy functional equation in probabilistic normed quasi-linear spaces by using a version of the fixed point theorem.

Keywords

• cauchy functional equation
• generalized hyers-ulam stabil- ity
• probabilistic quasi-linear space