Some fixed point results of F-Contraction mapping in D-metric spaces by Samet’s method

The aim of this paper is to study the F-contraction mapping introduced by Wardowski to obtain fixed point results by method of Samet in generalized complete metric spaces. Our findings extend the results announced by Samet methods and some other works in generalized metric spaces.

Knaster-Kuratowski-Mazurkiewicz Theorem in Generalized Metric Spaces with Applications

We study Knaster-Kuratowski-Mazurkiewicz theorem in the setting of generalized metric spaces. We establish some results on fixed points of Knaster-Kuratowski-Mazurkiewicz (KKM) mappings. Fan’s matching and Schauder’s type fixed point theorem in generalized metric spaces are also proved as interesting consequences of our main results. Examples are given to validate our results. We use these results to prove existence result for a given Atangana-Baleanu-Caputo fractional boundary value problem.

Statistical convergence in probabilistic generalized metric spaces w.r.t. strong topology

In this paper, the concept of probabilistic g-metric space with degree l, which is a generalization of probabilistic G-metric space, is introduced. Then, by endowing strong topology, the definition of l-dimensional asymptotic density of a subset A of $\mathbb{N}^{l}$ N l is used to introduce a statistically convergent and Cauchy sequence and to study some basic facts.

Conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory

In this paper we discuss similar problems posed by I. A. Rus in Fixed point theory in partial metric spaces (Analele Univ. de Vest Timişoara, Mat.-Inform., 46 (2008), 149–160) and in Kasahara spaces (Sci. Math. Jpn., 72 (2010), No. 1, 101–110). We start our considerations with an overview of generalized metric spaces with \mathbb{R}_+-valued distance and of generalized contractions on such spaces. After that we give some examples of conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory. Some possible applications to theoretical informatics are also considered.

Best Proximity Point Thorem For Generalized (

In this paper, we establish a new convergence theorem for best proximity of weak contractions in Branciari type generalized metric spaces under weak conditions.

Remarks of Fixed Point for ( ψ , φ )-Weakly Contractive Mappings

In this paper, we obtain a new fixed point theorem for weak contraction mappings on complete generalized metric spaces. Our result is different from that of ( ψ , φ )-weakly contractive mappings which had been obtained by Lakzian–Samet’s [Appl. Math. Lett. 25 (2012) 902–906]. Moreover, an example is given to illustrate the usability of the obtained result.

Fixed Point Results for C -Contractive Mappings in Generalized Metric Spaces with a Graph

In this paper, we establish fixed point theorems for Chatterjea contraction mappings on a generalized metric space endowed with a graph. Our results extend, generalize, and improve many of existing theorems in the literature. Moreover, some examples and an application to matrix equations are given to support our main result.

A fixed point theorem for generalized $(\psi ,\varphi )$-weak contractions in Branciari type generalized metric spaces

In this paper, we obtain a new convergence theorem for fixed points of weak contractions in Branciari type generalized metric spaces under weaker conditions. The proof process of the theorem is new and different from that of other authors. An illustrative example of this theorem is to show how the new conditions extend known results.