Abstract
In this paper, we present fixed point theorems for a generalized Roger Hardy type F-contraction in metric-like spaces and also give some examples to illustrate the main results in this paper. Moreover the applications of second-order differential equations and fractional differential equations are shown. The existing results improve and extend the corresponding results in the literature.
Highlights
Introduction and preliminaries InMethews (1994) extended the concept of a metric space to a partial metric space and obtained many results in partial metric spaces
We focus the fixed point theorem of generalized mappings in metric-like spaces
Main results First, we introduce the generalized Roger Hardy type F-contraction mapping in a metric-like space
Summary
Introduction and preliminaries InMethews (1994) extended the concept of a metric space to a partial metric space and obtained many results in partial metric spaces. Afterwards, many authors have studied the existence and uniqueness of a fixed point for nonlinear mappings satisfying various contractive conditions in the setting of partial metric spaces. We focus the fixed point theorem of generalized mappings in metric-like spaces. Shukla and Radenović (2013) have proved common fixed point theorems and introduced 0- -completeness in metric-like space which generalized Amini-Harandi’s results.
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