Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# 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 (doi: 10.20944/preprints201910.0301.v1). Saleh, W.; Kilicman, A. On the Characteristic Properties of Geodesic Sub-$(\alpha,b,s )$-Preinvex. Preprints 2019, 2019100301 (doi: 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.

## Subject Areas

E-convex sets; preinvex; E-convex functions; geodesic; sub-preinvex; Riemannian manifolds; Hadamard manifolds.

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