@article{Sangurlu_Turkoglu_2018, title={Some fixed point results in complete generalized metric spaces}, volume={9}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/1461}, DOI={10.15330/cmp.9.2.171-180}, abstractNote={<p>The Banach contraction principle is the most important result. This principle has many applications and some authors was interested in this principle in various metric spaces as Brianciari.</p> <p>The author initiated the notion of the generalized metric space as a generalization of a metric space by replacing the triangle inequality by a 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 introduced a new contraction, which generalizes the Banach contraction. He using a mapping $F: \mathbb{R}^{+} \rightarrow \mathbb{R}$ 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 show that the existence and uniqueness of fixed point for satisfying $F$-contraction and $F$-weak contraction in complete generalized metric spaces. Some examples are supplied in order to support the useability of our results. The obtained result is an extension and a generalization of many existing results in the literature.</p>}, number={2}, journal={Carpathian Mathematical Publications}, author={Sangurlu, S.M. and Turkoglu, D.}, year={2018}, month={Jan.}, pages={171–180} }