Hermite–Hadamard type inequalities for harmonic-arithmetic extended $ (s_1, m_1) $-$ (s_2, m_2) $ coordinated convex functions

Abstract

In this paper, the authors define the notion of harmonic-arithmetic extended $ (s_1, m_1) $-$ (s_2, m_2) $ coordinated convex functions, establish a new integral identity, present some new Hermite–Hadamard type integral inequalities for harmonic-arithmetic extended $ (s_1, m_1) $-$ (s_2, m_2) $ coordinated convex functions, and derive some known results.

Keywords

• hermite–hadamard type integral inequality
• harmonic-arithmetic extended $ (s_1， m_1) $-$ (s_2， m_2) $ coordinated convex function
• integral identity