Majorization-type inequalities for (m, M, ψ)-convex functions with applications

Abstract

In 2001, S. S. Dragomir introduced a generalized class of convexity, the so-called (m,M,ψ)\left(m,M,\psi )-convex functions, which covers many other classes of convexity. In this article, we prove some useful characterizations of this generalized class of convex functions. We obtain majorization-type inequalities for (m,M,ψ)\left(m,M,\psi )-convex functions, providing also applications to new estimates for some well-known mean inequalities.

Keywords

• convex function
• strongly convex function
• (m, m, ψ)-convex function
• majorization inequality
• sherman inequality
• 15b51
• 26d15
• 26a51
• 26e60