# Relation theoretic contraction results in $\mathcal{F}$-metric spaces

Volume 12, Issue 5, pp 337--344 Publication Date: January 11, 2019       Article History
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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

Jleli and Samet in [M. Jleli, B. Samet, J. Fixed Point Theory Appl., $\textbf{20}$ (2018), 20 pages] introduced a new metric space named as $\mathcal{F}$-metric space. They presented a new version of the Banach contraction principle in the context of this generalized metric spaces. The aim of this article is to define relation theoretic contraction and prove some generalized fixed point theorems in $\mathcal{F}$-metric spaces. Our results extend, generalize, and unify several known results in the literature.

### Keywords

• $\mathcal{F}$-metric space
• relation theoretic contractions
• fixed point
• binary relation

•  47H10
•  47H06

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