A new extension to the controlled metric type spaces endowed with a graph

Abstract

In this paper, we initiate a new extension of b-metric spaces, called controlled metric-like spaces, by changing the condition $$ \bigl[\wp (s,r)=0 \Leftrightarrow s=r\bigr]\quad \text{by } \bigl[\wp (s,r)=0 \Rightarrow s=r\bigr] $$ [ ℘ ( s , r ) = 0 ⇔ s = r ] by [ ℘ ( s , r ) = 0 ⇒ s = r ] and that means basically we may have a non-zero self-distance. We prove some fixed point theorems which generalize many results in the literature. Also, we present an interesting application to illustrate our results by considering controlled metric-like spaces endowed with a graph.

New Results in Controlled Metric Type Spaces

“…e concept of extended b-metric spaces was initiated by Kamran et al [8] in 2017, and their work generalized many results in the literature (see, for example, [12][13][14][15][16]). Definition 1 (see [8]).…”

Common Fixed Points of a Subfamily of a Nonexpansive Periodic Evolution Family on a Strictly Convex Banach Space

“…e study of fixed points has a large number of applications in differential equations, integral equations, and numerical equations. For more details, refer [15][16][17]. We also denote by X * the dual space of X.…”

Unique Fixed-Point Results in Fuzzy Metric Spaces with an Application to Fredholm Integral Equations

“…), mathematics, computer software, earth science, and physics. Some of their findings can be found in [18][19][20][21][22][23][24][25].…”