Geodesic $\gamma$-Pre-$E$-Convex Functions on Riemannian Manifolds
Received:July 28, 2022  Revised:January 08, 2023
Key Words: geodesic $E$-convex set   geodesic $\gamma$-pre-$E$-convex function   geodesic $\gamma$-$E$-convex function   optimality conditions  
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Author NameAffiliation
Seema MEENA Department of Mathematics, Faculty of Science, University of Rajasthan, Jaipur 302004, India 
D. B. OJHA 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.
Citation:
DOI:10.3770/j.issn:2095-2651.2023.03.007
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