GENERALIZED INVEX SETS AND PREINVEX FUNCTIONS ON RIEMANNIAN MANIFOLDS

被引：18

作者：

Agarwal, R. P. ^{[1
,2
]}

Ahmad, I. ^{[1
,3
]}

Iqbal, Akhlad ^{[4
]}

Ali, Shahid ^{[3
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, POB 728, Dhahran 31261, Saudi Arabia

[2] Texas A&M Univ, Dept Math, Kingsville, TX 78363 USA

[3] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

[4] BITS Pilani Hyderabad Compus, Dept Math, Hyderabad 500078, Andhra Pradesh, India

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2012年 / 16卷 / 05期

关键词：

Geodesic alpha-Invex sets; alpha-Invex functions; Geodesic alpha-Preinvex functions; Riemannian manifolds;

D O I：

10.11650/twjm/1500406792

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1719 / 1732

页数：14

共 16 条

[1] Mean value in invexity analysis [J].