IJPAM: Volume 116, No. 3 (2017)

Title

ON CONVEX FUNCTIONS, $E$-CONVEX FUNCTIONS AND
THEIR GENERALIZATIONS: APPLICATIONS TO
NON-LINEAR OPTIMIZATION PROBLEMS

Authors

S.N. Majeed$^1$, M.I. Abd Al-Majeed$^2$
$^{1,2}$Department of Mathematics
College of Education for Pure Sciences
(Ibn-Haitham), Baghdad University, Baghdad, IRAQ

Abstract

An important class of generalized convex sets and convex functions, called E-convex sets and E-convex functions, have been introduced and studied by Youness and other researchers. This class is proved to be useful in pure and applied mathematical fields. In this paper, some new characterizations of convex function, E-convex function, and their generalizations are discussed in terms of some level sets and different forms of epigraphs which are related to these functions. As an application of generalized convex functions in optimization problems, the optimality conditions of non-linear optimization problem using E-convex function (respectively, strictly E-convex function) and its generalizations such as E-quasiconvex function (respectively, strictly E-quasiconvex) function, and strictly quasi semi E-convex function are discussed.

History

Received: 2017-05-19
Revised: 2017-06-24
Published: October 26, 2017

AMS Classification, Key Words

AMS Subject Classification: 46N10, 47N10, 90C48, 90C90, 49K27
Key Words and Phrases: convex function, quasi convex function, E-convex function, E-convex set, slack 2-convex set, semi E-convex function

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How to Cite?

DOI: 10.12732/ijpam.v116i3.11 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 3
Pages: 655 - 673


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