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

[摘要] 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.

[学科分类] 电力

[关键词] GA-convex function;Jensen–Mercer inequality;Hadamard fractional integrals;Hermite–Hadamard inequality