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Abstract
E-convexity as a generalization of convexity has been introduced and studied in some recent publications in the fields of pure and applied mathematical analysis. In this study, some properties of E-convex and generalized E-convex functions are proved. Relationships between different notions are established and some clarifying examples are given. Finally, an application of the provided concepts, in multi-objective optimization, is addressed.
Acknowledgements
This research has been partially supported by the University of Tehran. The author thanks Professor George Loizou, Editor-in-Chief of IJCM, and the two anonymous referees for their constructive comments which contributed to the improvement of the present paper. Also, he would like to express his gratitude to Mr. Karim Rezaei for editing the English of the draft of this paper.