On Fixed-Point Results in Controlled Partial Metric Type Spaces with a Graph

Abstract

Recently, Mlaiki et al. introduced the notion of a controlled metric type space which is a generalization of the b-metric space. In this work, we define the controlled partial metric type space and give some fixed-point theorems for extensions of Kannan contraction in this space with suitable conditions. Moreover, as an application, we derive a fixed-point theorem for graphic contraction on the considered metric space endowed with a graph.

Controlled S-Metric-Type Spaces and Applications to Fractional Integrals

“…Thus, the existence of a unique solution ( 16) is equivalent to finding a unique fixed point of the integral operator (18). Consider…”

“…For example, some of them are given in [13,14]. Various generalizations of controlled metric-type spaces have also been defined [15][16][17][18]. Our motivation for this work is the S-metric spaces and controlled metric-type spaces we just mentioned.…”

Double Controlled Partial Metric Type Spaces and Convergence Results

“…Following that, in 2018, Abdeljawad et al [6,7] established the concepts of controlled metric type spaces and double controlled metric type spaces, respectively. Souayah and Mrad [8] proposed a more broad idea of controlled partial metric type spaces in 2019. It is useful to establish the extensions of the contraction principle from metric spaces to b-metric spaces, and therefore the controlled metric type of spaces is useful to prove the existence and uniqueness of theorems for many forms of integral and differential equations.…”