Abstract
This paper deals with some Fejer type inequalities related to (η1, η2)-convex functions. In fact the difference between the right and middle part of Fejer inequality is estimated without using Holder’s inequality when the absolute value of the derivative of considered function is (η1, η2)-convex. Furthermore we give two estimation results when the derivative of considered function is bounded and satisfies a Lipschitz condition.
Highlights
Introduction and Preliminaries TheFejer integral inequality for convex functions has been proved in [5]: Theorem 1.1
This paper deals with some Fejer type inequalities related to (η1, η2)-convex functions
Motivated by above works and references therein, we introduce the concept of (η1, η2)-convex functions as a generalization of preinvex and η-convex functions
Summary
Introduction and Preliminaries TheFejer integral inequality for convex functions has been proved in [5]: Theorem 1.1. The difference between the right and middle part of Fejer inequality is estimated without using Holder’s inequality when the absolute value of the derivative of considered function is (η1, η2)-convex. We give two estimation results when the derivative of considered function is bounded and satisfies a Lipschitz condition.
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