Jensen–Mercer inequality for GA-convex functions and some related inequalities

Abstract

Abstract In this paper, firstly, we prove a Jensen–Mercer inequality for GA-convex functions. After that, we establish weighted Hermite–Hadamard’s inequalities for GA-convex functions using the new Jensen–Mercer inequality, and we establish some new inequalities connected with Hermite–Hadamard–Mercer type inequalities for differentiable mappings whose derivatives in absolute value are GA-convex.

Keywords

• GA-convex function
• Jensen–Mercer inequality
• Hadamard fractional integrals
• Hermite–Hadamard inequality