Geodesic $E$-Invex Sets and Geodesic $E$-Preinvex Functions on Riemannian Manifolds
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Authors: Z. AMIRSHEKARI AND H. MOHEBI
DOI: 10.46793/KgJMat2401.067A
Abstract:
In this paper, we first introduce two new classes of sets and functions called geodesic E-invex sets and geodesic E-preinvex functions on a Riemannian manifold, respectively. Moreover, we present the definition and properties of geodesic E-quasi-preinvex functions on Riemannian manifolds. Finally, we investigate the properties and characterizations of these two classes of sets and functions.
Keywords:
Geodesic E-invex set, geodesic E-preinvex function, geodesic E-quasi-preinvex function, Riemannian manifold.
References:
[1] I. Akhlad, A. Shahid and I. Ahmad, On geodesic E-convex sets, geodesic E-convex functions and E-epigraphs, J. Optim. Theory Appl. 155 (2012), 239-251. https://doi.org/10.1007/s10957-012-0052-3
[2] I. Ahmad, I. Akhlad and A. Shahid, On properties of geodesic η-preinvex functions, Adv. Oper. Res. 2 (2009), 1–10. https://doi.org/10.1155/2009/381831
[3] R. P. Agarwal, I. Ahmad, A. Iqbal and A. Shahid,
Generalized invex sets and preinvex functions on Riemannian
manifolds, Taiwanese J. Math. 16(5) (2012), 1719–1732.
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