Non-existence of certain type of convex functions on a Riemannian manifold with a pole

被引：2
作者：
Shaikh, Absos Ali [1 ]
Mondal, Chandan Kumar [1 ]
Ahmad, Izhar [2 ]
机构：
[1] Univ Burdwan, Dept Math, Burdwan 713104, W Bengal, India
[2] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia
来源：
JOURNAL OF GEOMETRY AND PHYSICS | 2019年 / 140卷
关键词：
Convex function; Odd convex function; Even convex function; Manifold with a pole; Negative point of a manifold;
D O I：
10.1016/j.geomphys.2019.02.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to the study of non-existence of certain type of convex functions on a Riemannian manifold with a pole. To this end, we have developed the notion of odd and even functions on a Riemannian manifold with a pole and proved the non-existence of non-trivial and non-negative differentiable odd convex function whose gradient is complete. Finally, we have deduced an inequality related with convex function. (C) 2019 Elsevier B.V. All rights reserved.
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页码：104 / 110
页数：7
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