Abstract

In this paper, we prove a coupled fixed-point result for a hybrid mapping derived from generalized coupled Banach and Kannan-type contractions. We define the asymptotic regularity property for coupled maps and use it as a condition in our theorem. The results are derived in metric spaces with a preorder relation. The necessity of the hybrid contraction inequality is constrained by the preordering through the requirement that the inequality must be satisfied between points related by the preorder relation in a particular way. The main theorem is proven under several alternative additional conditions. There are several consequences of the main result, one of which is the relaxation of the contraction constant's range in the Kannan-type result. Two examples illustrate several features of the results presented herein. The paper concludes with an application to a system of integral equations.

Keywords: Asymptotic regularity; preorder; coupled $k$-continuity; coupled orbital continuity; coupled fixed point; Kannan-type contraction.

MSC: 47H10, 54H25, 54E50

DOI: 10.57016/MV-ZFQM4832

Pages:  1--12