Cauchy type means for some generalized convex functions

Matloob Anwar
Published: 1 July 2021

Abstract: In this paper, we establish Jensen’s inequality for s-convex functions in the first sense. By using Jensen’s inequalities, we obtain some Cauchy type means for p-convex and s-convex functions in the first sense. Also, by using Hermite–Hadamard inequalities for the respective generalized convex functions, we find new generalized Cauchy type means.
Keywords: Cauchy mean value theorem / Jensen’s inequality / Hermite–Hadamard inequality / p-convex function / s-convex function in the first sense