# Coincidence points of self mappings and left total relations

Volume 12, Issue 9, pp 582--588
Publication Date: May 03, 2019 Submission Date: January 25, 2019 Revision Date: February 21, 2019 Accteptance Date: April 04, 2019
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### Authors

Laila A. Alnaser - Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara, 41411, Kingdom of Saudi Arabia. Durdana Lateef - Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara, 41411, Kingdom of Saudi Arabia. Hoda A. Fouad - Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara, 41411, Kingdom of Saudi Arabia. - Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt. Jamshaid Ahmad - Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia.

### Abstract

The aim of this article is to prove some coincidence and fixed point theorems of hybrid contractions involving left total relations and single-valued mappings in the setting of $\mathcal{F}$-metric spaces which was first introduced by Jleli and Samet [M. Jleli, B. Samet, J. Fixed Point Theory Appl., $\textbf{20}$ (2018), 20 pages]. Finally, an example is also presented to verify the effectiveness and applicability of our main results.

### Keywords

• $\mathcal{F}$-metric space
• fixed point
• rational contraction

•  47H10
•  54H25

### References

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• [2] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundam. Math., 3 (1922), 133--181

• [3] A. Hussain, T. Kanwal, Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point results, Trans. A. Razmadze Math. Inst., 172 (2018), 481--490

• [4] M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 8 pages

• [5] M. Jleli, B. Samet, On a new generalization of Metric Spaces, J. Fixed Point Theory Appl., 20 (2018), 20 pages