Rectangular B-metric Spaces Research Articles

Fixed Point Results for Geraghty Type Contractions in Extended Rec-tangular Fuzzy <i>b</i>-metric Space with an Application

The aim of this paper is to define the notions of extended fuzzy b-metric spaces, fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces and to establish certain fixed point results in these settings utilizing Geraghty type contractions. We also furnished an example which illustrates our main result. To show the authenticity of our results we provide an application involving fuzzy integral equation. The obtained results generalize many existing results in the literature.

Common Fixed Point Theorems in Extended Rectangular b-Metric Spaces

In this paper, we establish common fixed point theorems for quadruple weakly compatible mappings satisfying a new generalized contraction condition. Our results generalize the corresponding result of Budi Nurwahyu et al. [6]. Non-trivial examples are further provided to support the hypotheses of our results.

Existence of coincidence and common fixed points for extended rectangular b-metric spaces

Existence of coincidence and common fixed points for extended rectangular b-metric spaces

Fixed Point Theorems in Rectangular b-Metric Space Endowed with a Partial Order

The purpose of this paper is to present some fixed-point results for self-generalized contractions in ordered rectangular b-metric spaces. We also provide some examples that illustrate the non-triviality and richness of this area of research.

Exploring Fuzzy Triple Controlled Metric Spaces: Applications in Integral Equations

In this article, we delve into the study of fuzzy triple controlled metric spaces, investigating their properties and presenting a range of illustrative examples. We emphasize the broader applicability of this concept in comparison to fuzzy rectangular metric spaces and fuzzy rectangular b-metric spaces. By introducing the novel concept of (α-ψ)-fuzzy contractive mappings, we derive fixed point results specifically designed for complete fuzzy triple controlled metric spaces. Our theorems extend and enrich previous findings in this field. Additionally, we demonstrate the practical significance of our study by applying our findings to the solution of an integral equation and providing an example of its application. Furthermore, we propose potential avenues for future research endeavors.

Stability analysis for complex-valued neural networks with fractional order

In the context of complex-valued rectangular b-metric spaces, the present study investigates the stability of complex-valued neural networks (CVNNs) with fractional order. Using the generalized contraction principle, we address the suitable condition for uniform stability of fractionally ordered CVNNs and establish the existence and uniqueness of the equilibrium point. Few numerical results are presented to show the feasibility and correctness of the results presented.

New fixed point theorems for $$(\phi , F)$$-contraction on rectangular b-metric spaces

New fixed point theorems for $$(\phi , F)$$-contraction on rectangular b-metric spaces

FIXED POINT RESULTS IN ORDERED EXTENDED RECTANGULAR b- METRIC SPACE WITH GERAGHTY-WEAK CONTRACTION

In this paper, we prove some ordered-theoretic fixed point results for a Geraghty-weak contraction on an ordered extended rectangular b􀀀metric spaces. Our results generalize several core results of the existing literature especially involving Geraghty-weak contractions and the results proved in extended rectangular b-metric space. Some examples are also furnished to exhibits the utility of our main results.

EXISTENCE AND UNIQUENESS OF FIXED POINT FOR NEW CONTRACTIONS IN RECTANGULAR b-METRIC SPACES

In this article, we give some new examples of rectangular b-metric spaces which are neither rectangular metric space nor metric space. After that we prove existence and uniqueness of new fixed points for some new contractions in rectangular b-metric spaces. Then we validate these results with suitable, appro- priate and innovative examples.

Relation-Theoretic Coincidence and Common Fixed Point Results in Extended Rectangular b-Metric Spaces with Applications

The objective of this paper is to obtain new relation-theoretic coincidence and common fixed point results for some mappings F and g via hybrid contractions and auxiliary functions in extended rectangular b-metric spaces, which improve the existing results and give some relevant results. Finally, some nontrivial examples and applications to justify the main results.

Fredholm Type Integral Equation in Controlled Rectangular Metric-like Spaces

In this article, we present an extension of the controlled rectangular b-metric spaces, so-called controlled rectangular metric-like spaces, where we keep the symmetry condition and we only change the condition [D(s,r)=0⇔s=r]to[D(s,r)=0⇒s=r], which means we may have a non-zero self distance; also, D(s,s) is not necessarily less than D(s,r). This new type of metric space is a generalization of controlled rectangular b-metric spaces and partial rectangular metric spaces.

Fixed point theorems for generalized (alpha ,psi )-contraction mappings in rectangular quasi b-metric spaces

In this paper, we introduce the class of rectangular quasi b-metric spaces as a generalization of rectangular metric spaces, rectangular quasi-metric spaces, rectangular b-metric spaces, define generalized (alpha ,psi ) -contraction mappings and study fixed point results for the maps introduced in the setting of rectangular quasi b-metric spaces. Our results extend and generalize related fixed point results in the literature, in particular, the works of Karapinar and Lakzian (J. Funct. Spaces 2014:914398, 2014), Alharbi et al. (J. Math. Anal. 9(3):47–60, 2018), and Khuangsatung et al. (Thai J. Math. 2020:89–101, 2020) from rectangular quasi metric space and rectangular b-metric space to rectangular quasi b-metric spaces. We also provide examples in support of our main findings. Furthermore, we applied one of our results to determine the existence of a solution to an integral equation.

Contraction Mappings in Intuitionistic Fuzzy Rectangular Extended B-Metric Spaces

In this study, we present the notion of intuitionistic fuzzy rectangular extended b-metric spaces as a generalization of intuitionistic fuzzy metric spaces and intuitionistic fuzzy rectangular b-metric spaces. Some well-known fixed-point results in metric fixed-point theory are generalized in the sense of intuitionistic fuzzy rectangular extended b-metric spaces. Several nontrivial examples and an application to nonlinear fractional differential equations are also imparted in this work to examine the validity of given results.

On the α−ψ−Contractive Mappings in C∗-Algebra Valued b-Rectangular Metric Spaces and Fixed Point Theorems

This present paper extends a version of α−ψ−contraction in C∗-algebra valued rectangular b-metric spaces and establishing the existence and uniqueness of fixed point for them. Non-trivial examples are further provided to support the hypotheses of our results.

Some New Aspects in the Intuitionistic Fuzzy and Neutrosophic Fixed Point Theory

In this manuscript, we use the concepts of continuous t-norms and continuous t-conorms to introduce some definitions, in which intuitionistic fuzzy rectangular metric spaces, intuitionistic fuzzy rectangular metric-like spaces, intuitionistic fuzzy rectangular b-metric spaces, intuitionistic fuzzy rectangular b-metric-like spaces, neutrosophic rectangular metric spaces, neutrosophic rectangular metric-like spaces, neutrosophic rectangular b-metric spaces, and neutrosophic rectangular b-metric-like spaces are included. Continuous t-norms and continuous t-conorms are used to generalize the probability distribution of triangular inequalities in metric space axioms. Nontrivial examples, some fixed point results, and an application to the integral equation are imparted in this manuscript.

The Sehgal’s Fixed Point Result in the Framework of ρ-Space

In this paper, we prove a fixed point theorem of Sehgal type (see Sehgal, V.M., Proc Amer Math Soc 23: 631–634, 1969) in a more general setting of ρ-space (see Secelean, N.A. and Wardowski, D., Results Math, 72: 919–935, 2017). In this way, we can find, as particular cases, some results of Sehgal type in metric, b-metric and rectangular b-metric spaces.

On Fuzzy Extended Hexagonal b-Metric Spaces with Applications to Nonlinear Fractional Differential Equations

The focus of this research article is to investigate the notion of fuzzy extended hexagonal b-metric spaces as a technique of broadening the fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces as well as to derive the Banach fixed point theorem and several novel fixed point theorems with certain contraction mappings. The analog of hexagonal inequality in fuzzy extended hexagonal b-metric spaces is specified as follows utilizing the function b(c,d): mhc,d,t+s+u+v+w≥mhc,e,tb(c,d)∗mhe,f,sb(c,d)∗mhf,g,ub(c,d)∗mhg,k,vb(c,d)∗mhk,d,wb(c,d) for all t,s,u,v,w>0 and c≠e,e≠f,f≠g,g≠k,k≠d. Further to that, this research attempts to provide a feasible solution for the Caputo type nonlinear fractional differential equations through effective applications of our results obtained.

F-contractions Fixed point results in Extended Rectangular b-metric space

In the present paper, we prove common fixed point theorem for F-contraction by considering one map is orbitally continuous map in $Omega-$Extended rectangular b-metric space. In addition, we find fixed point for Banach and Kannan type contraction inequality without consideration of orbitally continuity. Also at the fixed point maps does not force to be continuous. An examples is also provided for the utility of our results.

Fixed point theorems for ψ−contractive mapping in C∗−algebra valued rectangular b-metric spaces

In this paper, we present a new insight of C∗−algebra valued rectangular b−metric spaces in the perspective of the fixed point theory using contractive mapping. Using contractive mapping in the rectangular b−metric spaces, we discussed the existence and the uniqueness of the fixed point with mapping satisfying a contractive condition. As a result, we obtained an interesting and important result for the general case of C∗−algebra valued metric spaces. In particular, we study some fixed point theorems in the C∗−algebra valued rectangular b−metric spaces using a positive function.

Fixed Point Results via α-Admissibility in Extended Fuzzy Rectangular b-Metric Spaces with Applications to Integral Equations

In this article, the concept of extended fuzzy rectangular b-metric space (EFRbMS, for short) is initiated, and some fixed point results frequently used in the literature are generalized via α-admissibility in the setting of EFRbMS. For the illustration of the work presented, some supporting examples and an application to the existence of solutions for a class of integral equations are also discussed.