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On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs

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Abstract

In this paper, we introduce a new class of sets and a new class of functions called geodesic E-convex sets and geodesic E-convex functions on a Riemannian manifold. The concept of E-quasiconvex functions on R n is extended to geodesic E-quasiconvex functions on Riemannian manifold and some of its properties are investigated. Afterwards, we generalize the notion of epigraph called E-epigraph and discuss a characterization of geodesic E-convex functions in terms of its E-epigraph. Some properties of geodesic E-convex sets are also studied.

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Acknowledgements

The authors are highly thankful to anonymous referees and the editor for their valuable suggestions/comments which have contributed to the final preparation of the paper.

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Author notes

  1. Akhlad Iqbal

    Present address: Department of Mathematics, BITS Pilani Hyderabad Campus, Hyderabad, AP, India

  2. I. Ahmad

    Present address: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Akhlad Iqbal, Shahid Ali & I. Ahmad

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  1. Akhlad Iqbal
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  2. Shahid Ali
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Correspondence to Akhlad Iqbal.

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Communicated by Horst Martini.

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Iqbal, A., Ali, S. & Ahmad, I. On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs. J Optim Theory Appl 155, 239–251 (2012). https://doi.org/10.1007/s10957-012-0052-3

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  • DOI: https://doi.org/10.1007/s10957-012-0052-3

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