Generalization, Refinement and Reverses of the Right Fejer Inequality for ´ Convex Functions

Authors

  • Silvestru Sever Dragomi (1) Mathematics, School of Engineering & Science Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia. (2) DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences School of Computer Science & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa.

Keywords:

Convex functions, Integral inequalities, Jensen’s type inequalities, Fejer type ´ inequalities, Lebesgue integral, Hermite-Hadamard type inequalities, Special means

Abstract

In this paper we establish a generalization of the right Fejer´ inequality for general Lebesgue integral on measurable spaces as well as a positive lower bound and some upper bounds for the difference h (a) + h (b) 2 − 1 R b a g (x) dx Z b a h (x) g (x) dx, where h : [a, b] → R is a convex function and g : [a, b] → [0, ∞) is an integrable weight. Applications for discrete means are also provided.

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Published

2017-12-31

Issue

Vol. 49 No. 3 (2017)

Section

Articles

How to Cite

Generalization, Refinement and Reverses of the Right Fejer Inequality for ´ Convex Functions. (2017). Punjab University Journal of Mathematics, 49(3), 1-13. https://pujm.pu.edu.pk/index.php/pujm/article/view/102