Application of Fixed Point Results for Modified Generalized F-Contraction Mappings to Solve Boundary Value Problems

Abstract

The aim of this paper is to introduce the notion of (α, β)-cyclic admissible mapping and modified generalized F-contraction mapping in the framework of metric-like spaces. Fixed point theorems for modified generalized F-contraction mapping in complete metric-like spaces are established. Furthermore, we present examples to support our main results, using these examples, we establish that our main results is a generalization of the fixed point result of Karapinar et al. [Fixed points of conditionally-contractions in complete metric-like spaces, Fixed Point Theory, and Appl. 2015] and a host of others in the literature. As an application, we apply our result to find the existence of a solution to second-order differential equations. Finally, we correct an anomaly detected in the work of Karapinar et al.[17]. Our results improve and extend corresponding results in the literature.