Complementarity problems via common fixed points in vector lattices

Fixexd point theory and applications

Abdul Rahim Khan¹  Mujahid Abbas²  SZ Né³ 

[1] Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia;Lahore University of Management Sciences (LUMS), Lahore, Pakistan;School of Mathematics, The University of Birmingham, Birmingham, UK

关键词: coincidence point equation;    weak order contractive condition;    order convergence;    vector lattice;    mutually dominating maps;   

DOI  :  10.1186/1687-1812-2012-60

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Nemeth introduced the notion of order weakly L-Lipschitz mapping and employed this concept to obtain nontrivial solutions of nonlinear complementarity problems. In this article, we shall extend this concept to two mappings and obtain the solution of common fixed point equations and hence coincidence point equations in the framework of vector lattices. We present some examples to show that the solution of nonlinear complementarity problems and implicit complementarity problems can be obtained using these results. We also provide an example of a mapping for which the conclusion of Banach contraction principle fails but admits one of our fixed point results. Our proofs are simple and purely order-theoretic in nature.

【 授权许可】

CC BY