Abstract

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.

Details

Title
A new extension to the controlled metric type spaces endowed with a graph
Author
Mlaiki Nabil 1 ; Souayah Nizar 2 ; Thabet, Abdeljawad 3 ; Hassen, Aydi 4   VIAFID ORCID Logo 

1  Prince Sultan University, Department of Mathematics and General Sciences, Riyadh, Saudi Arabia (GRID:grid.443351.4) (ISNI:0000 0004 0367 6372) 
2  King Saud University, Department of Natural Sciences, Community College Al-Riyadh, Riyadh, Saudi Arabia (GRID:grid.56302.32) (ISNI:0000 0004 1773 5396) 
3  Prince Sultan University, Department of Mathematics and General Sciences, Riyadh, Saudi Arabia (GRID:grid.443351.4) (ISNI:0000 0004 0367 6372); China Medical University, Department of Medical Research, Taichung, Taiwan (GRID:grid.254145.3) (ISNI:0000 0001 0083 6092); Asia University, Department of Computer Sciences and Information Engineering, Taichung, Taiwan (GRID:grid.252470.6) (ISNI:0000 0000 9263 9645) 
4  China Medical University, Department of Medical Research, Taichung, Taiwan (GRID:grid.254145.3) (ISNI:0000 0001 0083 6092); Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse, Tunisia (GRID:grid.7900.e) (ISNI:0000 0001 2114 4570); Sefako Makgatho Health Sciences University, Department of Mathematics and Applied Mathematics, Ga-Rankuwa, South Africa (GRID:grid.459957.3) (ISNI:0000 0000 8637 3780) 
Publication year
2021
Publication date
Feb 2021
Publisher
Springer Nature B.V.
ISSN
1687-1839
e-ISSN
1687-1847
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1186/s13662-021-03252-9
ProQuest document ID
2485325416
Copyright
© The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.