| Geodesic $\gamma$-Pre-$E$-Convex Functions on Riemannian Manifolds |
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| 作者姓名： | Seema MEENA D. B. OJHA |
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| 作者单位： | Department of Mathematics, Faculty of Science, University of Rajasthan, Jaipur 302004, India |
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| 摘 要： | In this paper, we generalize geodesic $E$-convex function and define geodesic $\gamma$-pre-$E$-convex and geodesic $\gamma$-$E$-convex functions on Riemannian manifolds. The sufficient condition of equivalence class of geodesic $\gamma$-pre-$E$-convexity and geodesic $\gamma$-$E$-convexity for differentiable function on Riemannian manifolds is studied. We discuss the sufficient condition for $E$-epigraph to be geodesic $E$-convex set. At the end, we establish some optimality results with the aid of geodesic $\gamma$-pre-$E$-convex and geodesic $\gamma$-$E$-convex functions and discuss the mean value inequality for geodesic $\gamma$-pre-$E$-convex function.
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| 关 键 词： | geodesic $E$-convex set geodesic $\gamma$-pre-$E$-convex function geodesic $\gamma$-$E$-convex function optimality conditions |
| 收稿时间： | 2022/7/28 0:00:00 |
| 修稿时间： | 2023/1/8 0:00:00 |
Geodesic $\gamma$-Pre-$E$-Convex Functions on Riemannian Manifolds |
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| Seema MEENA,D. B. OJHA.Geodesic $\gamma$-Pre-$E$-Convex Functions on Riemannian Manifolds[J].Journal of Mathematical Research with Applications,2023,43(3):324-334. |
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| Authors: | Seema MEENA D B OJHA |
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| Affiliation: | Department of Mathematics, Faculty of Science, University of Rajasthan, Jaipur 302004, India |
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| Abstract: | In this paper, we generalize geodesic $E$-convex function and define geodesic $\gamma$-pre-$E$-convex and geodesic $\gamma$-$E$-convex functions on Riemannian manifolds. The sufficient condition of equivalence class of geodesic $\gamma$-pre-$E$-convexity and geodesic $\gamma$-$E$-convexity for differentiable function on Riemannian manifolds is studied. We discuss the sufficient condition for $E$-epigraph to be geodesic $E$-convex set. At the end, we establish some optimality results with the aid of geodesic $\gamma$-pre-$E$-convex and geodesic $\gamma$-$E$-convex functions and discuss the mean value inequality for geodesic $\gamma$-pre-$E$-convex function. |
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| Keywords: | geodesic $E$-convex set geodesic $\gamma$-pre-$E$-convex function geodesic $\gamma$-$E$-convex function optimality conditions |
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