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Abstract and Applied Analysis
Volume 2016, Article ID 4652038, 7 pages
http://dx.doi.org/10.1155/2016/4652038
Research Article

On Certain Properties for Two Classes of Generalized Convex Functions

Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt

Received 31 March 2016; Accepted 4 May 2016

Academic Editor: Wing-Sum Cheung

Copyright © 2016 Mohamed S. S. Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Two classes of generalized convex functions in the sense of Beckenbach are considered. For both classes, we show that the existence of support curves implies their generalized convexity and obtain an extremum property of these functions. Furthermore, we establish Hadamard’s inequality for them.