Complementarity problems via common fixed points in vector lattices

Mujahid Abbas, Abdul Rahim Khan*, S. Z. Németh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number60
JournalFixed Point Theory and Applications
Volume2012
DOIs
Publication statusPublished - 2012

Bibliographical note

Funding Information:
The authors are thankful to the anonymous referees for their critical remarks which helped to improve the presentation of the paper. A. R. Khan is grateful to King Fahd University of Petroleum and Minerals for supporting the research project IN101037. M. Abbas was supported by Higher Education Commission, Pakistan.

Keywords

  • Coincidence point equation
  • Mutually dominating maps
  • Order convergence
  • Vector lattice
  • Weak order contractive condition

ASJC Scopus subject areas

  • Geometry and Topology
  • Applied Mathematics

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