On the existence of solutions of generalized equilibrium problems with \(\alpha-\beta-\eta\)-monotone mappings

Volume 9, Issue 10, pp 5712--5719 http://dx.doi.org/10.22436/jnsa.009.10.16

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Authors

A. Farajzadeh - Department of Mathematics, Razi University, Kermanshah 67149, Iran. S. Plubtieng - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand. - Center of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand. A. Hosseinpour - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand. - Center of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.

Abstract

The present paper is concerned with the new concept of relaxed \(\alpha-\beta-\eta\)-monotonicity and relaxed \(\alpha-\beta-\eta\)-pseudomonotonicity in Banach space which is applied to prove the existence of solutions of generalized equilibrium problem and classic equilibrium problem. In this regard, we use the well-known KKM-theory to obtain solutions of mentioned problems.

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Keywords

• KKM-mappings
• hemicontinuity
• \(\alpha-\beta-\eta\)-monotonicity
• \(\alpha-\beta-\eta\)-pseudomonotonicity
• semicontinuous mappings
• Banach space.

MSC

•  47H05
•  49J40

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