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The main aim of this work is to study multivalued HR-type interpolative contraction and multivalued P-contraction through (H,F)-contraction and C-class function, respectively via Maia type result in b-metric spaces setting. Moreover, by using the notion of multi-valued triangular α-admissible mappings of type Δ, we have investigated our new findings. Some related fixed point results for such mappings are also proved in this set-up. Our results extend, generalize and modify many famous results that exist in the literature. We furnish an example to justify our new findings. As an application, we implement our results in data dependence and stability of fixed point. [ABSTRACT FROM AUTHOR]

Abstract In this study, we manifest a new class of mappings that satisfy Geraghty–Ćirić-type contractive conditions in the context of b-metric spaces and prove a theorem on the existence and uniqueness of fixed points. Our results unify and generalize the results of Geraghty; Ćirić; Dukic, Kadelburg, and Radenović; and Shu-fang Li, Fei Hi, and Ning Lu in the setting of b-metric spaces. Furthermore, we provide examples to verify the correctness and applicability of our results. We also utilize our findings to show the existence of a unique solution for a nonlinear integral equation.

Abstract In this paper, we introduce the notion of generalized ( α , ϕ ) $(\alpha , \phi )$ -Meir–Keeler hybrid contractive mappings of type I and II via simulation function and establish fixed point theorems for such mappings in the setting of complete b-metric spaces. Our results extend and generalize many related fixed point results in the existing literature. Finally, we provide an example in support of our main finding.

In this study, we manifest a new class of mappings that satisfy Geraghty–Ćirić-type contractive conditions in the context of b-metric spaces and prove a theorem on the existence and uniqueness of fixed points. Our results unify and generalize the results of Geraghty; Ćirić; Dukic, Kadelburg, and Radenović; and Shu-fang Li, Fei Hi, and Ning Lu in the setting of b-metric spaces. Furthermore, we provide examples to verify the correctness and applicability of our results. We also utilize our findings to show the existence of a unique solution for a nonlinear integral equation. [ABSTRACT FROM AUTHOR]

Since the topological properties of a b-metric space (which generalizes the concept of a metric space) seem sometimes counterintuitive due to the fact that the "open" balls may not be open sets, we review some aspects of these spaces concerning compactness, metrizability, continuity and fixed points. After doing so, we introduce new types of contractivities that extend the concept of Banach contraction. We study some of their properties, giving sufficient conditions for the existence of fixed points and common fixed points. Afterwards, we consider some iterative schemes in quasi-normed spaces for the approximation of these critical points, analyzing their convergence and stability. We apply these concepts to the resolution of a model of integral equation of Urysohn type. In the last part of the paper, we refine some results about partial contractivities in the case where the underlying set is a strong b-metric space, and we establish some relations between mutual weak contractions and quasi-contractions and the new type of contractivity. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized (α , ϕ) -Meir–Keeler hybrid contractive mappings of type I and II via simulation function and establish fixed point theorems for such mappings in the setting of complete b-metric spaces. Our results extend and generalize many related fixed point results in the existing literature. Finally, we provide an example in support of our main finding. [ABSTRACT FROM AUTHOR]

In this paper, in the first part, we will improve and extend the main results 1 and 2 of Mishra et al. [6] in a b-metric space, and in the second and last part, we will improve and extend Theorem 5 and Theorem 6 of Shah [7] in a b-metric-like space, in both sections, we will use our new notion of occasionally weakly biased maps of type (풜). Some illustrative examples are given in order to clarify and support our findings. [ABSTRACT FROM AUTHOR]

In this manuscript, we present a novel notion of α -βM-Geraghty type contractions, which are employed to establish the existence and uniqueness of a fixed point in complete bmetric spaces. To emphasize the significance of our results, illustrative examples are provided. Furthermore, we utilize the obtained results to demonstrate the existence of a solution for matrix equations. Thus, our results provide a suitable extension in this respect. [ABSTRACT FROM AUTHOR]

In this paper, we present a sufficient condition for the unique existence of solutions for a coupled system of nonlinear fractional Langevin equations with a new class of multipoint and nonlocal integral boundary conditions. We define a Zλ*-contraction mapping and present the sufficient condition by identifying the problem with an equivalent fixed point problem in the context of b-metric spaces. Finally, some numerical examples are given to validate our main results. [ABSTRACT FROM AUTHOR]

In this manuscript, we obtain a fixed point theorem for set-valued quasi-contraction maps in complete b -metric spaces of zero at infinity varieties. We present some example satisfiyes the theorem. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new fixed point result for Hardy-Rogers type contractions in double controlled metric-like spaces. Our result generalizes many important theorems in the literature. We will provide an example to illustrate our results.

Since the topological properties of a b-metric space (which generalizes the concept of a metric space) seem sometimes counterintuitive due to the fact that the “open” balls may not be open sets, we review some aspects of these spaces concerning compactness, metrizability, continuity and fixed points. After doing so, we introduce new types of contractivities that extend the concept of Banach contraction. We study some of their properties, giving sufficient conditions for the existence of fixed points and common fixed points. Afterwards, we consider some iterative schemes in quasi-normed spaces for the approximation of these critical points, analyzing their convergence and stability. We apply these concepts to the resolution of a model of integral equation of Urysohn type. In the last part of the paper, we refine some results about partial contractivities in the case where the underlying set is a strong b-metric space, and we establish some relations between mutual weak contractions and quasi-contractions and the new type of contractivity.

The authors explore fixed-point theory in b-metric spaces and strong b-metric spaces. They wish to prove some new extensions of the Covitz and Nadler fixed-point theorem in b-metric spaces. In so doing, they wish to answer a question proposed by Kirk and Shahzad about Nadler’s theorem holding in strong b-metric spaces. In addition, they offer an improvement to the fixed-point theorem proven by Dontchev and Hager.

In this paper, we present some results on the existence and uniqueness of common fixed points on d * -complete topological spaces. Our results generalize and improve upon earlier results in the literature. Finally, we give some examples in l p spaces, (p ∈ (0 , 1)) , where we use the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we firstly introduce definition of weak interpolative Hardy-Rogers type contractions and we give an example for a class of this mappings. We also prove a fixed point theorem under some appropriate conditions on complete b-metric spaces. Finally, we discuss an application to homotopy theory of our main result. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new fixed point result for Hardy-Rogers type contractions in double controlled metric-like spaces. Our result generalizes many important theorems in the literature. We will provide an example to illustrate our results. [ABSTRACT FROM AUTHOR]

The concept of an F-contraction was introduced by Wardowski, while Samet et al. introduced the class of α-admissible mappings and the concept of (α-ψ)-contractive mapping on complete metric spaces. In this paper, we study and extend two types of contraction mappings: (α-ψ)-contraction mapping and (α-F)-contraction mapping, and establish new fixed point results on double controlled metric type spaces. Moreover, we demonstrate some examples and present an application of our result on the existence and uniqueness of the solution for an integral equation.

Abstract In the present paper the concepts of q-rung orthopair fuzzy mappings (q-ROF mapping) and q-rung ( α , β ) $( \alpha ,\beta ) $ -cuts are introduced. Some common fixed point results for q-ROF mappings are presented in b-metric spaces using Suzuki-type contractive conditions. Examples in support of obtained results are also presented. We have also presented an application of our result for the existence of solution of nonlinear fractional integral inclusion. The results are of their own kind in the literature of q-ROF sets and will pave the way for further research in the area.

This paper surveys regarding solutions of linear and nonlinear integral equations through fixed point theorem. Banach's contraction mapping principle is the most widely applied fixed point theorem in all of analysis with special applications to the theory of integral equations. Over a decade researchers have generalized the definition of a metric space and using the technique of fixed point have found solutions to many linear and nonlinear Volterra-Fredholm integral equations.

The double-controlled metric-type space (X , D) is a metric space in which the triangle inequality has the form D (η , μ) ≤ ζ 1 (η , θ) D (η , θ) + ζ 2 (θ , μ) D (θ , μ) for all η , θ , μ ∈ X . The maps ζ 1 , ζ 2 : X × X → [ 1 , ∞) are called control functions. In this paper, we introduce a novel generalization of a metric space called a double-composed metric space, where the triangle inequality has the form D (η , μ) ≤ α D (η , θ) + β D (θ , μ) for all η , θ , μ ∈ X . In our new space, the control functions α , β : [ 0 , ∞) → [ 0 , ∞) are composed of the metric D in the triangle inequality, where the control functions ζ 1 , ζ 2 : X × X → [ 1 , ∞) in a double-controlled metric-type space are multiplied with the metric D. We establish some fixed-point theorems along with the examples and applications. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of an optimum solution of a system of ordinary differential equations via the best proximity points. In order to obtain the optimum solution, we have developed the best proximity point results for generalized multivalued contractions of b-metric spaces. Examples are given to illustrate the main results and to show that the new results are the proper generalization of some existing results in the literature. [ABSTRACT FROM AUTHOR]

In the paper, we apply some of the results from the theory of ball spaces in semimetric setting. This allows us to obtain fixed point theorems which we believe to be unknown to this day. As a byproduct, we obtain the equivalence of some different notions of completeness in semimetric spaces where the distance function is 1-continuous. In the second part of the article, we generalize the Caristi–Kirk results for b-metric spaces. Additionally, we obtain a characterization of semicompleteness for 1-continuous b-metric spaces via a fixed point theorem analogous to a result of Suzuki. In the epilogue, we introduce the concept of convergence in ball spaces, based on the idea that balls should resemble closed sets in topological sets. We prove several of its properties, compare it with convergence in semimetric spaces and pose several open questions connected with this notion. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend some fixed point results from [Şerban, M. A., Teoria punctului fix pentru operatori definiți pe produs cartezian, Presa Universitară Clujeană, Cluj-Napoca, 2002] and [Prešić, S. B., Sur une classe d' inéquations aux différences finite et sur la convergence de certaines suites, Publ. Inst. Math. (Beograd) (N. S.). 5(19) (1965), 75-78] in the framework of b-metric spaces. [ABSTRACT FROM AUTHOR]

In the present paper the concepts of q-rung orthopair fuzzy mappings (q-ROF mapping) and q-rung (α , β) -cuts are introduced. Some common fixed point results for q-ROF mappings are presented in b-metric spaces using Suzuki-type contractive conditions. Examples in support of obtained results are also presented. We have also presented an application of our result for the existence of solution of nonlinear fractional integral inclusion. The results are of their own kind in the literature of q-ROF sets and will pave the way for further research in the area. [ABSTRACT FROM AUTHOR]

This manuscript was originally built to establish some coupled common fixed point results for rational contractive mapping in the framework of b-metric spaces. Thereafter, the existence and uniqueness of the boundary value problem for a singular coupled fractional differential equation of order ν via coupled fixed point techniques are discussed. At the last, some supportive examples to illustrate the theoretical results are presented.

In this paper, we prove some common fixed point theorems satisfying contractive type mapping in the setting of b-metric spaces. The presented theorem is an extension the results of M. Sarwar and M. U. Rahman [23] as well as a generalization of many well-known results in the literature through the context of b-metric spaces. Also, we present a few examples to illustrate the validity of the results obtained in the paper. Finally, results are applied to find the solution for an integral equation.

In this paper, we present some results on the existence and uniqueness of common fixed points on d*-complete topological spaces. Our results generalize and improve upon earlier results in the literature. Finally, we give some examples in lp spaces, (p∈(0,1)), where we use the obtained results.

We establish a new fixed point theorem in the setting of convex b-metric spaces that ensures the existence of fixed point for Cirić contraction with the assumption k<1s2. Also, the fixed point is approximated by Krasnoselskij iterative procedure. Moreover, we discuss the stability of fixed point for the aforesaid contraction. As a consequence, we develop a common fixed point and coincidence point result. Finally, we provide a number of examples to illustrate the findings presented here and incorporate these findings to solve an initial value problem.

An iterated function system consists of a complete metric space (X,d) and a finite family of contractions f1,⋯,fn:X→X. A generalized iterated function system comprises a finite family of contractions defined on the Cartesian product Xm with values in X. In this paper, we want to investigate generalized iterated function systems in the more general setting of b-metric spaces. We prove that such a system admits a unique attractor and, under some further restrictions on the b-metric, it depends continuously on parameters. We also provide two examples of generalized iterated function systems defined on a particular b-metric space and find the corresponding attractors.

Abstract This article examines new multivalued interpolative Reich–Rus–Ćirić-type contraction conditions and fixed point results for multivalued maps that fulfill these conditions. Earlier defined interpolative contraction type conditions cannot be particularized to any contraction type condition. This slackness of the interpolative contraction type condition is addressed through new multivalued interpolative Reich–Rus–Ćirić-type contraction conditions.

In this paper, we introduce a new concept of locally α-ψ-contractive mapping, generalized α−ψ rational contraction and establish fixed point theorems for such mappings in the setting of extended b-metric space. Our main results extend and improve some results given by some authors. We also provide a non trivial example to show the validity of our main results. As an application, we derive some new fixed point result for ψ-graphic contraction defined on an extended b-metric space endowed with a graph.

Abstract In this paper, we initiate a new extension of b-metric spaces, called controlled metric-like spaces, by changing the condition [ ℘ ( s , r ) = 0 ⇔ s = r ] by [ ℘ ( s , r ) = 0 ⇒ s = r ] $$ \bigl[\wp (s,r)=0 \Leftrightarrow s=r\bigr]\quad \text{by } \bigl[\wp (s,r)=0 \Rightarrow s=r\bigr] $$ and that means basically we may have a non-zero self-distance. We prove some fixed point theorems which generalize many results in the literature. Also, we present an interesting application to illustrate our results by considering controlled metric-like spaces endowed with a graph.

The double-controlled metric-type space (X,D) is a metric space in which the triangle inequality has the form D(η,μ)≤ζ1(η,θ)D(η,θ)+ζ2(θ,μ)D(θ,μ) for all η,θ,μ∈X. The maps ζ1,ζ2:X×X→[1,∞) are called control functions. In this paper, we introduce a novel generalization of a metric space called a double-composed metric space, where the triangle inequality has the form D(η,μ)≤αD(η,θ)+βD(θ,μ) for all η,θ,μ∈X. In our new space, the control functions α,β:[0,∞)→[0,∞) are composed of the metric D in the triangle inequality, where the control functions ζ1,ζ2:X×X→[1,∞) in a double-controlled metric-type space are multiplied with the metric D. We establish some fixed-point theorems along with the examples and applications.

This paper surveys regarding solutions of linear and nonlinear integral equations through fixed point theorem. Banach’s contraction mapping principle is the most widely applied fixed point theorem in all of analysis with special applications to the theory of integral equations. Over a decade researchers have generalized the definition of a metric space and using the technique of fixed point have found solutions to many linear and nonlinear Volterra-Fredholm integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of mappings called the weak KKH-Caristi type expansion in b-metric and ordered b-metric spaces by generalizing the Caristi-type contractions. Also, we present some fixed point results on this class of mappings. Some examples are also given to support and illustrate our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some fixed point results for surrounding quasi-contractions in non-triangular metric spaces. Also, we prove the Banach principle of contraction in non-triangular metric spaces. As applications of our theorems, we deduce certain well-known results in b-metric spaces as corollaries.

Abstract In this paper, we introduce a new extension of the double controlled metric-type spaces, called double controlled metric-like spaces, by assuming that the “self-distance” may not be zero On the other hand, if the value of the metric is zero, then it has to be a “self-distance” (i.e., we replace [ ς ( g , h ) = 0 ⇔ g = h ] $[\varsigma(g,h)=0 \Leftrightarrow g=h]$ by [ ς ( g , h ) = 0 ⇒ g = h ] $[\varsigma(g,h)=0 \Rightarrow g=h]$ ). Using this new type of metric spaces, we generalize many results in the literature. We prove fixed point results along with examples illustrating our theorems. Also, we present double controlled metric-like spaces endowed with a graph along with an open question.

This paper deals with the existence of an optimum solution of a system of ordinary differential equations via the best proximity points. In order to obtain the optimum solution, we have developed the best proximity point results for generalized multivalued contractions of b-metric spaces. Examples are given to illustrate the main results and to show that the new results are the proper generalization of some existing results in the literature.

We present a significant example to show that the class of v-generalized b-metric spaces properly contains the class of v-generalized metric spaces as well as b-metric spaces. This is accomplished because the example provided by Došenović et al. (2020) is insufficient to expose the generality of v-generalized b-metric spaces over the existing related spaces. Therefore, we establish fixed point theorems by defining generalized almost contractions of rational type and Reich type in v-generalized b-metric spaces. Moreover, we compare the proven results with the already existing fixed point theorems in this space by presenting suitable examples. As a consequence of these fixed point theorems, we further develop some common fixed-point results that ensure the existence and uniqueness of coincidence points and common fixed points for a pair of self maps. Finally, we use the outcome to check that the given Fredholm integral equation has a solution and that it is also unique.

In this paper, we present some fixed point results for Subrahmanyan contraction in the setting of a b-metric space. We consider the case of multivalued operators. We also deduce the Ulam–Hyers stability property of the fixed point inclusion. The notion of b-metric generalizes the one of a metric, as in the third condition, the right-hand side is multiplied by a real number greater than 1. We remark that the second axiom, i.e., the one which shows the symmetry of the b-metric, remains unchanged. The findings presented in this paper extend some recent results which were proved in the context of a metric space. Some open questions are presented at the end of the paper.

In this paper, we establish some fixed point theorems with the help of α-admissible mapping satisfying (ψ,Φ) contractive condition of integral type in Gb-metric space. Our results are supported by examples. [ABSTRACT FROM AUTHOR]

In this study, we utilize the notion of triple controlled metric type space that preserves the symmetry property, which is a generalization of b-metric-type spaces, to prove new fixed-point results. We introduce (α-F)-contractive mappings and Θ-contractive mappings on triple controlled metric type space settings. Then, we establish the existence and uniqueness of fixed-point results on complete triple controlled metric type space. Moreover, some examples and applications to boundary-value problems of the fourth-order differential equation are presented to display the usage of the obtained result.

The purpose of this work is to introduce the new concept of a hybrid JS-contraction in b-metric spaces which includes various contractions in such spaces. The existence and uniqueness of a fixed point for self mappings satisfying the proposed contractive condition on b-metric spaces are studied. As an application, the existence result of a unique solution for integral equations is also given in order to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an extension of metric spaces, which includes S spaces. Some properties of this topological structure are analyzed. Also, a non-compactness measure and condensing correspondences are defined for these type of spaces and natural results are obtained. Moreover, fixed point theorems for functions and correspondences satisfying certain Banach orbital condition are introduced and proved. These results are applied to contractions, which are defined by means of the extended quasi-metric, both for functions and correspondences. [ABSTRACT FROM AUTHOR]

This article examines new multivalued interpolative Reich–Rus–Ćirić-type contraction conditions and fixed point results for multivalued maps that fulfill these conditions. Earlier defined interpolative contraction type conditions cannot be particularized to any contraction type condition. This slackness of the interpolative contraction type condition is addressed through new multivalued interpolative Reich–Rus–Ćirić-type contraction conditions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a common fixed point problem for two pairs {f, S} and {g, T} of weakly compatible selfmaps of a complete b-metric (X, d; s), satisfying a contractive condition of Ćirić type. This contraction and some of its variants were used in the paper [29] published in 2016 by V. Ozturk and S. Radenovic, requiring the (E.A.)-property for the pairs {f, S} and {g, T}. The aim of this paper is to provide some improvements to the main result of [29]. Our main theorem will improve certain results published in 2015, by V. Ozturk and D. Turkoglu (see [30] and [31]). We improve also results from other related papers (see the references herin). Indeed, we remove the (E.A.)property and weaken certain assumptions imposed in these papers. So, our work aims to extend and unify, in one go, several common fixed point results known in a recent literature. We furnish two illustrative examples and we prove that the fixed point problem, considered here, for the pairs {f, S} and {g, T} is well-posed. We compare our main result with a recent result obtained in 2018 by N. Hussain, Z. D. Mitrović and S. Radenović in [19].

In this paper, we introduce some new types of extended Geraghty contractions, called (α,β)-admissible generalized Geraghty F-contractions, and prove some fixed point results for such contractions in the setting of partial b-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point result for graphic generalized Geraghty F-contractions defined on partial metric spaces endowed with a directed graph. As an application, we examine the existence of a unique solution to the first-order periodic boundary value by the obtained fixed point result. Moreover, some examples are presented to illustrate the validity of the new results.

In this paper, we present some fixed point theorems for a class of contractive mappings in complete b-metric spaces of zero at infinity varieties. We verify the T-stability of Picard's iteration and the P property for such mapping. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the results of coincidence and common fixed points in b-metric spaces. We work with a new type of multivalued quasi-contractive mapping with nonlinear comparison functions. Our results generalize and improve several recent results. Additionally, we give an application of the obtained results to dynamical systems.

Our paper is devoted to the issue of the existence and uniqueness of common fixed points for two mappings in complete b-metric spaces by virtue of the new functions F and θ, respectively. Moreover, two specific examples to indicate the validity of our results are also given. Eventually, the generalized forms of Jungck fixed point theorem in the above spaces is investigated. Different from related literature, the conditions that the function F needs to satisfy are weakened, and F only needs to be non-decreasing in this paper. To some extent, our conclusions and methods improve the results of previous literature.