Generalized vector equilibrium problems on Hadamard manifolds

Volume 9, Issue 3, pp 1402--1409 http://dx.doi.org/10.22436/jnsa.009.03.64

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Authors

Shreyasi Jana - Department of Mathematics, Indian Institute of Technology Kharagpur, 721302 Kharagpur, India. Chandal Nahak - Department of Mathematics, Indian Institute of Technology Kharagpur, 721302 Kharagpur, India. Cristiana Ionescu - Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania.

Abstract

In this paper, we study several types of Generalized Vector Equilibrium Problems (GVEP) on Hadamard manifolds. We prove sufficient conditions under which the solution set of (GVEP)'s is nonempty. As an application, we prove existence theorems for the system of generalized vector variational inequality problems and the system of generalized Pareto optimization problems.

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Keywords

• Hadamard manifold
• variational inequality
• equilibrium problem
• KKM mapping.

MSC

•  47H05
•  58A05
•  58B20
•  90C33

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