Cyclic Mappings and Further Results in B-Metric-Like Spaces

Fixed point problem of many mappings has been widely studied in the research work of fixed point theory. The generalized metric space is one of the research objects of fixed point theory. B-metric-like space is one of the generalized metric spaces; in fact, the research work in B-metric-like spaces is attractive. The intention of this paper is to introduce the concept of other cyclic mappings, named as L β -type cyclic mappings in the setting of B-metric-like space, study the existence and uniqueness of fixed point problem of L β -type cyclic mapping, and obtain some new results in B-metric-like spaces. Furthermore, the main results in this paper are illustrated by a concrete example. The work of this paper extend and promote the previous results in B-metric-like spaces.

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.

Hyperspace of finite unions of convergent sequences

The symbol S(X) denotes the hyperspace of finite unions of convergent sequences in a Hausdor˛ space X. This hyper-space is endowed with the Vietoris topology. First of all, we give a characterization of convergent sequence in S(X). Then we consider some cardinal invariants on S(X), and compare the character, the pseudocharacter, the sn-character, the so-character, the network weight and cs-network weight of S(X) with the corresponding cardinal function of X. Moreover, we consider rank k-diagonal on S(X), and give a space X with a rank 2-diagonal such that S(X) does not Gδ -diagonal. Further, we study the relations of some generalized metric properties of X and its hyperspace S(X). Finally, we pose some questions about the hyperspace S(X).

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.

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.