Geodesic r -preinvex functions on Riemannian manifolds

Journal of inequalities and applications

Meraj Ali Khan¹ 

关键词: invex sets;    preinvex functions;    r-invexity;    Riemannian manifolds;   

DOI  :  10.1186/1029-242X-2014-144

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we introduce a new class of functions called r-invexity and geodesic r-preinvexity functions on a Riemannian manifolds. Further, we establish the relationships between r-invexity and geodesic r-preinvexity on Riemannian manifolds. It is observed that a local minimum point for a scalar optimization problem is also a global minimum point under geodesic r-preinvexity on Riemannian manifolds. In the end, a mean value inequality is extended to a Cartan-Hadamard manifold. The results presented in this paper extend and generalize the results that have appeared in the literature. MSC:58E17, 90C26.

【 授权许可】

CC BY