TY - JOUR
T1 - A new extension to the controlled metric type spaces endowed with a graph
AU - Mlaiki, Nabil
AU - Souayah, Nizar
AU - Abdeljawad, Thabet
AU - Aydi, Hassen
N1 - Publisher Copyright:
© 2021, The Author(s).
PY - 2021/12
Y1 - 2021/12
N2 - In this paper, we initiate a new extension of b-metric spaces, called controlled metric-like spaces, by changing the condition [℘(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.
AB - In this paper, we initiate a new extension of b-metric spaces, called controlled metric-like spaces, by changing the condition [℘(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.
KW - Controlled metric type space
KW - Controlled metric-like space
KW - Extended b-metric space
KW - Fixed point
KW - b-metric spaces
UR - http://www.scopus.com/inward/record.url?scp=85100277549&partnerID=8YFLogxK
U2 - 10.1186/s13662-021-03252-9
DO - 10.1186/s13662-021-03252-9
M3 - Article
AN - SCOPUS:85100277549
SN - 1687-1839
VL - 2021
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 94
ER -