Existence Theorems for Coincidence Points of f-Contractive Mappings in Cone b-Metric Spaces

Watcharapong Anakkamatee, Kasamsuk Ungchittrakool

Abstract

In this paper, two f-contractive mappings are provided and studied in cone b-metric spaces. The first one is called f-contractive mapping of type B and the second one is called f-contractive mapping of type KC, respectively. Under some available properties on a complete cone b-metric space, some suitable conditions on scalars and the considered two new f-contractive mappings T, we can generate a Cauchy sequence to find and confirm the existence of a coincidence point of f and $T$ without the assumption of normality. The obtained results not only directly improve and generalize some fixed point results in metric spaces and b-metric spaces but also expand and complement some previous results in cone metric spaces.