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In an article published in 2015, Hussain et al. introduced a notion of a fuzzy b-metric space and obtained some fixed point theorems for this kind of space. Shortly thereafter, Nădăban presented a notion of a fuzzy b-metric space that is slightly different from the one given by Hussain et al., and explored some of its topological properties. Related to Nădăban's study, Sedghi and Shobe, Saadati, and Šostak independently conducted investigations in articles published in 2012, 2015, and 2018, respectively, about another class of spaces that Sedgi and Shobe called b-fuzzy metric spaces, Saadati, fuzzy metric type spaces, and Šostak, fuzzy k-metric spaces. The main contributions of our paper are the following: First, we propose a notion of fuzzy b-metric space that encompasses and unifies the aforementioned types of spaces. Our approach, which is based on Gabriec's notion of a fuzzy metric space, allows us to simultaneously cover two interesting classes of spaces, namely, the 01-fuzzy b-metric spaces and the K-stationary fuzzy b-metric spaces. Second, we show that each fuzzy b-metric space, in our sense, admits uniformity with a countable base. From this fact, we derive, among other consequences, that the topology induced by means of its "open" balls is metrizable. Finally, we obtain a characterization of complete fuzzy b-metric spaces with the help of a fixed point result which is also proved here. In support of our approach, several examples, including an application to a type of difference equations, are discussed. [ABSTRACT FROM AUTHOR]

In this paper we consider a kind of Geraghty contractions by using m w -distances in the setting of complete quasi-metric spaces. We provide fixed point theorems for this type of mappings and illustrate with some examples the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we enlarge the class of C * -algebra valued partial metric spaces as well as the class of C * -algebra valued b-metric spaces by introducing the class of C * -algebra valued partial b-metric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result in order to examine the existence and uniqueness of a solution for the system of Fredholm integral equations. [ABSTRACT FROM AUTHOR]

The purpose of this manuscript is to provide much simpler and shorter proofs of some recent significant results in the context of generalized F-Suzuki-contraction mappings in b-complete b-metric spaces. By using our new approach for the proof that a Picard sequence is b-Cauchy, our results generalize, complement and improve many known results in the existing literature. Further, some new contractive conditions are provided here to illustrate the usability of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued ( Θ , δ b )-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of our main result, we present the sufficient conditions for the existence of solutions of Fredholm integral inclusions. An example is also provided to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of α -almost Istrăt̨escu contraction of type E and of type E ∗ in the setting of b-metric space. The existence of fixed points for such mappings is investigated and some examples to illustrate the validity of the main results are considered. In the last part of the paper, we list some immediate consequences. [ABSTRACT FROM AUTHOR]

The aim of this manuscript is to get the strong convergence theorems of the Moudafi's viscosity approximation methods for an asymptotically nonexpansive nonself mapping in C A T (0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we enlarge the classes of rectangular M b -metric spaces and extended rectangular b-metric spaces by considering the class of extended rectangular M r ξ -metric spaces and utilize the same to prove an analogue of Banach contraction principle in such spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of solution for a system of Fredholm integral equation. [ABSTRACT FROM AUTHOR]

In this manuscript, we consider some hybrid contractions that merge linear and nonlinear contractions in the abstract spaces induced by the Branciari distance and the Branciari b-distance. More precisely, we introduce the notion of a (p , c) -weight type ψ -contraction in the setting of Branciari distance spaces and the concept of a (p , c) -weight type contraction in Branciari b-distance spaces. We investigate the existence of a fixed point of such operators in Branciari type distance spaces and illustrate some examples to show that the presented results are genuine in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize the F -contractive condition in the framework of α − ν -complete modular b-metric spaces. Some results in ordered modular b-metric spaces are also presented. Moreover, an illustrative example and some related applications are presented to support the obtained results. [ABSTRACT FROM AUTHOR]

Recently, George et al. (in Georgea, R.; Radenovicb, S.; Reshmac, K.P.; Shuklad, S. Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 2015, 8, 1005–1013) furnished the notion of rectangular b-metric pace (RBMS) by taking the place of the binary sum of triangular inequality in the definition of a b-metric space ternary sum and proved some results for Banach and Kannan contractions in such space. In this paper, we achieved fixed-point results for a pair of F-dominated mappings fulfilling a generalized rational F-dominated contractive condition in the better framework of complete rectangular b-metric spaces complete rectangular b-metric spaces. Some new fixed-point results with graphic contractions for a pair of graph-dominated mappings on rectangular b-metric space have been obtained. Some examples are given to illustrate our conclusions. New results in ordered spaces, partial b-metric space, dislocated metric space, dislocated b-metric space, partial metric space, b-metric space, rectangular metric spaces, and metric space can be obtained as corollaries of our results. [ABSTRACT FROM AUTHOR]

In this paper, using an interpolative approach, we investigate two fixed point theorems in the framework of a b-metric space whose all closed and bounded subsets are compact. One of the theorems is for set-valued Hardy–Rogers-type and the other one is for set-valued Reich–Rus–Ćirić-type contractions. Examples are provided to validate the results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider various results in the context of G b -metric spaces that have been recently published after the paper (Aghajani, A.; Abbas, M.; Roshan, J.R. Common fixed point of generalized weak contractive mappings in partially ordered G b -metric spaces. Filomat 2014, 28, 1087–1101). Our new results improve, complement, unify, enrich and generalize already well known results on G b -metric spaces. Moreover, some coupled and tripled coincidence point results have been provided. [ABSTRACT FROM AUTHOR]

In this paper, we prove new fixed-point theorems using the set of simulation functions on an S-metric space with some illustrative examples. Our results are stronger than some known fixed-point results. Furthermore, we give an application to the fixed-circle problem with respect to a simulation function. [ABSTRACT FROM AUTHOR]

In this manuscript, we introduce the notion of b-hybrid contraction in the setting of b-metric space. We investigate the existence and uniqueness of a fixed point for this contraction. Our results combine and merge several existing results in the corresponding literature and we list some of them as corollaries. Finally, we consider an Ulam's type stability for an application. [ABSTRACT FROM AUTHOR]

In this paper, we present the concept of Θ − (σ , ξ) Ω -contraction mappings and we nominate some related fixed point results in ordered p-metric spaces. Our results extend several famous ones in the literature. Some examples and an application are given in order to validate our results. [ABSTRACT FROM AUTHOR]

This article intends to initiate the study of Pompeiu–Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent examples and a result on homotopy. This approach improves the current state of art in fixed point theory. [ABSTRACT FROM AUTHOR]

We improve and generalize some new results in fixed point theory in the context of partial b-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, by characterizing a weak contractive condition based on using C − functions and α − admissible multi-valued mapping of type S, we present some fixed point results for (α , F) − admissible multi-valued mappings in the setting of b − metric spaces. Some examples and an application are added in order to show the reliability of our obtained results. Our results amend, unify, and generalize some existing results in the literature. The scientific novelty of our main results is to take new contraction self-mappings in b − metric spaces for multi-valued mappings. [ABSTRACT FROM AUTHOR]