Some fixed point results in complete generalized metric spaces
Journal Title: Карпатські математичні публікації - Year 2017, Vol 9, Issue 2
Abstract
The Banach contraction principle is the important result, that has many applications. Some authors\- were interested in this principle in various metric spaces. Branciari A. initiated the notion of the generalized metric space as a generalization of a metric space by replacing the triangle inequality by more general inequality, $d(x,y)\leq d(x,u)+d(u,v)+d(v,y)$ for all pairwise distinct points $x,y,u,v$ of $X$. As such, any metric space is a generalized metric space but the converse is not true. He proved the Banach fixed point theorem in such a space. Some authors proved different types of fixed point theorems by extending the Banach's result. Wardowski D. introduced new contraction which generalizes the Banach contraction. Using a mapping $F: \mathbb{R}^{+} \rightarrow \mathbb{R}$ he introduced a new type of contraction called $F$-contraction and proved a new fixed point theorem concerning $F$-contraction. In this paper, we have dealt with $F$-contraction and $F$-weak contraction in complete generalized metric spaces. We prove some results for $F$-contraction and $F$-weak contraction and we establish the existence and uniqueness of fixed point for $F$-contraction and $F$-weak contraction in complete generalized metric spaces. Some examples are supplied in order to support the usability of our results. The obtained result is an extension and a generalization of many existing results in the literature.
Authors and Affiliations
S. M. Sangurlu, D. Turkoglu
Keywords
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- EP ID EP325362
- DOI 10.15330/cmp.9.2.171-180
- Views 75
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