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On the Characteristic Properties of Geodesic Sub-$ (\alpha,b,s )$-Preinvex
Version 1
: Received: 26 October 2019 / Approved: 27 October 2019 / Online: 27 October 2019 (10:41:01 CET)
How to cite: Saleh, W.; Kilicman, A. On the Characteristic Properties of Geodesic Sub-$ (\alpha,b,s )$-Preinvex. Preprints 2019, 2019100301. https://doi.org/10.20944/preprints201910.0301.v1 Saleh, W.; Kilicman, A. On the Characteristic Properties of Geodesic Sub-$ (\alpha,b,s )$-Preinvex. Preprints 2019, 2019100301. https://doi.org/10.20944/preprints201910.0301.v1
Abstract
In the present work we study the properties of geodesic sub-$ (\alpha,b,s) $-preinvex functions on Hadamard manifolds and establish some basic properties in both general and differential cases. Further, we study sufficient conditions of optimality and proved some new inequalities under geodesic sub-($ \alpha,b,s $)-preinvexity.
Keywords
E-convex sets; preinvex; E-convex functions; geodesic; sub-preinvex; Riemannian manifolds; Hadamard manifolds.
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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