Abstract
In this paper, a geodesic $\alpha$-invex subset of a Riemannian manifold is introduced. Geodesic $\alpha$-invex and $\alpha$-preinvex functions on a geodesic $\alpha$-invex set with respect to particular maps are also defined. Further, we study the relationships between geodesic $\alpha$-invex and $\alpha$-preinvex functions on Riemannian manifolds. Some results of a non smooth geodesic $\alpha$-preinvex function are also discussed using proximal subdifferentiation. At the end, mean value inequality and the mean value theorem in $\alpha$-invexity analysis are extended to Cartan-Hadamard manifolds. Our results extend and generalize the known results in the literature.
Citation
R. P. Agarwal. I. Ahmad. Akhlad Iqbal. Shahid Ali. "GENERALIZED INVEX SETS AND PREINVEX FUNCTIONS ON RIEMANNIAN MANIFOLDS." Taiwanese J. Math. 16 (5) 1719 - 1732, 2012. https://doi.org/10.11650/twjm/1500406792
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