Generalization and reverses of the left Fejer inequality for convex functions

Volume 10, Issue 6, pp 3231--3244 http://dx.doi.org/10.22436/jnsa.010.06.35

Publication Date: June 25, 2017 Submission Date: April 18, 2017

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Authors

S. S. Dragomir - Mathematics, School of Engineering & Science, Victoria University, P. O. Box 14428, Melbourne City, MC 8001, Australia. - chool of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa.

Abstract

In this paper we establish a generalization of the left Fej´er inequality for general Lebesgue integral on measurable spaces as well as various upper bounds for the difference \[\frac{1}{\int^b_a g(x)dx} \int^b_ah(x)g(x)dx-h\left(\frac{a+b}{2}\right),\] where \(h : [a, b] \rightarrow \mathbb{R}\) is a convex function and \(g : [a, b] \rightarrow [0,\infty)\) is an integrable weight. Applications for discrete means and Hermite-Hadamard type inequalities are also provided.

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Keywords

• Convex functions
• integral inequalities
• Jensen’s type inequalities
• Fejér type inequalities
• Lebesgue integral
• Hermite-Hadamard type inequalities
• special means.

MSC

•  26D15
•  26D20

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