Hyers-Ulam Stability of Jensen Functional Inequality in p-Banach Spaces

Abstract

We prove the Hyers-Ulam stability of the following Jensen functional inequality $\parallel f((x-y)/n+z)+f((y-z)/n+x)+f((z-x)/n+y)\parallel \le \parallel f((x+y+z)\parallel$ in $p$-Banach spaces for any fixed nonzero integer $n$.