Some Further Results Using Green’s Function for s -Convexity

Abstract

For s-convex functions, the Hermite–Hadamard inequality is already well-known in convex analysis. In this regard, this work presents new inequalities associated with the left-hand side of the Hermite–Hadamard inequality for s-convexity by utilizing a novel technique based on Green’s function. Also, Hölder, Young, and power-mean inequalities are used to obtain these new inequalities. Finally, some applications to special means of real numbers are provided. In conclusion, we think that the methodology used in this work will encourage more research in this field.