Order-clustered fixed point theorems and their applications to Pareto equilibrium problems


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	Order-clustered fixed point theorems and their applications to Pareto equilibrium problems


	Fixed Point Theory, Volume 18, No. 2, 2017, 755-772, June 1st, 2017 DOI: 10.24193/fpt-ro.2017.2.61 Authors: Linsen Xie, Jinlu Li, Adrian Petrușel and Jen-Chih Yao Abstract: In this paper, we provide some properties of order clusters in preordered sets and we prove some order-clustered fixed point theorems on preordered sets. Then by applying these theorems, we show the existence of ordered Pareto equilibrium and Nash equilibrium for some noncooperative strategic games with incomplete (preordered) preferences. Key Words and Phrases: Chain-complete preordered sets, order-clustered fixed point, fixed point, Pareto equilibrium, Nash equilibrium. 2010 Mathematics Subject Classification: 46B42, 47H10, 91A06. Published on-line: June 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents