On Geodesic <Emphasis Type="Italic">E</Emphasis>-Convex Sets,Geodesic <Emphasis Type="Italic">E</Emphasis>-Convex Functions and <Emphasis Type="Italic">E</Emphasis>-Epigraphs |
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| Authors: | Akhlad Iqbal Shahid Ali I Ahmad |
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| Institution: | 1.Department of Mathematics,Aligarh Muslim University,Aligarh,India;2.Department of Mathematics,BITS Pilani Hyderabad Campus,Hyderabad,India;3.Department of Mathematics and Statistics,King Fahd University of Petroleum and Minerals,Dhahran,Saudi Arabia |
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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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