Approximation of general 3-variable Jensen $\rho$-functional inequalities in complex Banach spaces

TL;DR

This paper introduces a new 3-variable Jensen $ ho$-functional equation and proves its stability in complex Banach spaces, expanding the understanding of functional inequalities in advanced mathematical contexts.

Contribution

It presents the first investigation into the stability of 3-variable Jensen $ ho$-functional inequalities in complex Banach spaces.

Findings

Established Hyers-Ulam stability for the 3-variable Jensen $ ho$-functional equations.

Extended the theory of Jensen functional inequalities to complex Banach spaces.

Provided foundational results for future research in functional analysis and inequality stability.

Abstract

In this paper, we introduce and investigate general 3-variable Jensen $\rho$-functional equation, and prove the Hyers-Ulam stability of the Jensen functional equations associated with the general 3-variable Jensen $\rho$-functional inequalities in complex Banach spaces.