Order-Lipschitz mappings restricted with linear bounded mappings in normed vector spaces without normalities of involving cones via methods of upper and lower solutions

Abstract

In this paper, without assuming the normalities of cones, we prove some new fixed point theorems of order-Lipschitz mappings restricted with linear bounded mappings in normed vector space in the framework of w-convergence via the method of upper and lower solutions. It is worth mentioning that the unique existence result of fixed points in this paper, presents a characterization of Picard-completeness of order-Lipschitz mappings.