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

Abstract

We prove the Hyers-Ulam stability of the following Jensen functional inequality∥f((x-y)/n+z)+f((y-z)/n+x)+f((z-x)/n+y)∥≤∥f((x+y+z)∥inp-Banach spaces for any fixed nonzero integern.

A Fixed Point Approach to Stability of Additive Functional Inequalities in Fuzzy Normed Spaces

“…and Kim, Jun, and Son [13] proved the generalized Hyers-Ulam stability of the Jensen functional inequality in p-Banach spaces. Banachs contraction principle is one of the pivotal results of analysis.…”

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

“…Recently, H. Kim and E. Son [9], proved the generalized Hyers-Ulam stability for the following Jensen type functional inequality…”

Generalized Hyers-Ulam Stability of Quadratic Functional Inequality

“…Fechner [18] and Gilányi [19] have proved the generalized Hyers-Ulam stability of the functional inequality (2). Park et al [20] have investigated the generalized Hyers-Ulam stability of functional inequalities associated with Jordanvon Neumann type additive functional equations, and Kim et al [21] have proved the generalized Hyers-Ulam stability of Jensen functional inequality in -Banach spaces. The stability problems of several functional equations and inequalities have been extensively investigated by a number of authors and there are many interesting results concerning the stability of various functional equations and inequalities [6,22].…”