Abstract
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.
Highlights
Introduction and preliminaries LetE be a vector space
If ≤ is a partial order on E, E is called ordered vector space and the set K = {x Î E : 0 ≤ x} is a cone called the positive cone of E
It is known that x* is a solution of the nonlinear complementarity problem defined by K and f if and only if x* is a fixed point of the mapping
Summary
Introduction and preliminaries LetE be a vector space. A closed convex set K in E is called closed convex cone, if for any l > 0 and x Î K, lx Î K. A monotone increasing mapping : K ® K is called (c)-comparison operator if there exists an order convergent series xn in K and a real number a Î [0,1) such that k+1(t) ≤ ak(t) +
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