ADDITIVE FUNCTIONAL INEQUALITIES IN PARANORMED SPACES

Abstract

In this paper, we investigate the following additive functional inequalities parallel to 1/s f(x) + 1/s f(y) + f(z) + f(w)parallel to <= parallel to f (x+y/s + z + w)parallel to, parallel to 1/s f(x) + 1/s f(y) + 1/s f(z) + f(w)parallel to <= parallel to f(x+y+z/s + w)parallel to in paranormed spaces for a fixed integer s greater than 1. Furthermore, we prove the Hyers-Ulam stability of the above additive functional inequalities in paranormed spaces.