The Borwein-Preiss variational principle for nonconvex countable systems of equilibrium problems

Volume 9, Issue 5, pp 2224--2232 http://dx.doi.org/10.22436/jnsa.009.05.26

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Authors

Somyot Plubtieng - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand. - Research center for Academic Excellence in Nonlinear Analysis and Optimization, Naresuan University. Thidaporn Seangwattana - Research center for Academic Excellence in Nonlinear Analysis and Optimization, Naresuan University.

Abstract

The aim of the present paper, by using the Borwein-Preiss variational principle, we prove existence results for countable systems of equilibrium problems. We establish some sufficient conditions which can guarantee two existence theorems for countable systems of equilibrium problems on closed subsets of complete metric spaces and on weakly compact subsets of real Banach spaces, respectively.

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Keywords

• Borwein-Preiss variational principle
• bifunction
• complete metric space
• equilibrium problems
• gauge-type function
• nonconvex.

MSC

•  47H10
•  54H25

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