M φ M ψ $M_{\varphi}M_{\psi}$ -convexity and separation theorems

Abstract

Abstract A characterization of pairs of functions that can be separated by an M φ M ψ $M_{\varphi}M_{\psi}$ -convex function and related results are obtained. Also, a Hyers–Ulam stability result for M φ M ψ $M_{\varphi}M_{\psi}$ -convex functions is given.

Keywords

• M φ M ψ $M_{\varphi}M_{\psi}$ -convex function
• Separation theorem
• Hyers–Ulam stability
• Quasi-arithmetic mean