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This paper combines the concept of an arbitrary binary connection with the widely recognized principle of θ -contraction to investigate the innovative features of vector-valued metric spaces. This methodology demonstrates the existence of fixed points for both single- and multi-valued mappings within complete vector-valued metric spaces. Through the utilization of binary relations and θ -contraction, this study advances and refines the Perov-type fixed-point results in the literature. Furthermore, this article furnishes examples to substantiate the validity of the presented results. Additionally, we establish an application for finding the existence of solutions to a system of matrix equations. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the recent advances in the fixed point theory. Some discussions are presented on the relation of fixed point theorems to applications, and areas are delineated in the future research directions as well. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the regularity of nonnegative solutions of Lane-Emden system {−Δu = vp −Δv = uq in Rn. By means of Kelvin transform, we turn this problem into estimating the local integrability of (u,v). Assume that (u,v) possesses some initial local integrability beforehand.(u,v) ∈ Lr0loc(Rn) × Ls0loc(Rn) for any suitable r0 and s0 under specified conditions. Then through a regularity lifting method by contracting operators, we prove that(u,v) ∈ Lrloc(Rn) × Lsloc(Rn) for r and s sufficiently large under twice regularity lifting if needed. Furthermore, we lift the regularity of solutions to L∞(Rn) × L∞(Rn). We believe that these new methods employed in this paper can be widely applied to study a variety of other problems with different spaces and linear or nonlinear problems. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]

In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those are contained in Berzig [J. Fixed Point Theory Appl. 12, 221-238 (2012))] and Alam and Imdad [To appear in Filomat (arXiv:1603.09159 (2016))]. Interestingly, a corollary to one of our main results under symmetric closure of a binary relation remains a sharpened version of a theorem due to Berzig. Finally, we use examples to highlight the accomplished improvements in the results of this paper. [ABSTRACT FROM AUTHOR]

It follows from [A. L. Dontchev, R. T. Rockafellar, Springer, New York, (2014), Theorem 5I.3] that the distance from a point x to the set of fixed points of a set-valued contraction mapping Φ is bounded by a constant times the distance from x to Φ(x). In this paper, we generalize both this result and Lim's lemma for a larger class of set-valued mappings instead of the class of set-valued contraction mappings. As consequence, we obtain some known fixed points theorems. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well-known contraction conditions in one go besides yielding several new ones. We also provide an example to demonstrate the generality of our results over several well-known corresponding results of the existing literature. Finally, we utilize our results to prove an existence theorem for ensuring the solution of an integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new contractive mappings in the setup of completeness and uniqueness of fixed point theorem on b-metric space. We improve the recent fixed point results established by Agrawal et al. (Agrawal, S., Qureshi, K. and Nema, J., A fixed point theorems for b-metric space, IJPAM, 9(1), 2016, 45-50). We also show that different contractive type mappings exist in b-metric space. [ABSTRACT FROM AUTHOR]

In this paper, based on some geometrical properties of CAT p (0) spaces, for p ≥ 2 , we obtain two fixed point results for monotone multivalued nonexpansive mappings and proximally monotone nonexpansive mappings. Which under some assumptions, reduce to coincide and generalize a fixed point result for monotone nonexpansive mappings. This work is a continuity of the previous work of Ran and Reurings, Nieto and Rodríguez-López done for monotone contraction mappings. [ABSTRACT FROM AUTHOR]

In this paper, we define the concepts of ϕ-contraction in probabilistic generalized Menger space. We prove that ϕ-contraction mappings in probabilistic generalized Menger space have a unique fixed point. Also we prove some fixed point theorems related this concept. Some examples are given to support the obtained results. [ABSTRACT FROM AUTHOR]

In this article, we have extended the results of Y. U. Gaba by taking multiplicative -metric space instead of -metric space. In this way, we proved contraction mapping theorems on multiplicative, -metric spaces using rational type contraction conditions for a single map. Later on, we extended our results in the settings of triplet maps. We have also given examples to support our results. [ABSTRACT FROM AUTHOR]

In this paper it is shown that a classical continuation principle due to Granas for contractions holds under weaker contractive assumptions. This leads to a Leray-Schauder principle for such contractions in hyperbolic spaces. Some applications to nonexpansive mappings in hyperbolic geodesic spaces are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of common limit range ((CLR)-property) in the framework of quasi-partial metric spaces. By using this concept, some fixed point theorems involving two pairs of contraction mappings are proved without using the com- pleteness condition of the whole space. Our results extend some results in literature, such as Nazir and Abbas [8] and Vetro et al. [11]. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of $(\alpha,\psi)$-rational type contractive mappings and provide sufficient conditions for the existence and uniqueness of a fixed point for such class of generalized nonlinear contractive mappings in the setting of generalized metric spaces. We also deduce several interesting corollaries. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Banach contraction principle to metric-like as well as partial metric spaces (not essentially complete) equipped with an arbitrary binary relation. Thereafter, we derive some fixed point results which are sharper versions of the corresponding known results of the existing literature. Finally, we use some examples to demonstrate the usability and generality of our main result. [ABSTRACT FROM AUTHOR]

The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing the fixed-stress split scheme, which leads to an iteratively solved semi-discrete system. The error bounds are derived by combining a posteriori estimates for contractive mappings with functional type error control for elliptic partial differential equations. The estimates are applicable to any approximation in the admissible functional space and are independent of the discretization method. They are fully computable, do not contain mesh-dependent constants, and provide reliable global estimates of the error measured in the energy norm. Moreover, they suggest efficient error indicators for the distribution of local errors and can be used in adaptive procedures. [ABSTRACT FROM AUTHOR]

In this paper, we present yet another new and novel variant of classical Banach contraction principle on a complete metric space endowed with a binary relation which, under universal relation, reduces to Banach contraction principle. In process, we observe that various kinds of binary relations, such as partial order, preorder, transitive relation, tolerance, strict order, symmetric closure, etc., utilized by earlier authors in several well-known metrical fixed point theorems can be weakened to the extent of an arbitrary binary relation. [ABSTRACT FROM AUTHOR]

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In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those are contained in Berzig [J. Fixed Point Theory Appl. 12, 221-238 (2012))] and Alam and Imdad [To appear in Filomat (arXiv:1603.09159 (2016))]. Interestingly, a corollary to one of our main results under symmetric closure of a binary relation remains a sharpened version of a theorem due to Berzig. Finally, we use examples to highlight the accomplished improvements in the results of this paper.

In this manuscript, we prove the existence and uniqueness of a common best proximity point for a pair of non-self mappings satisfying the iterative mappings in a complete fuzzy multiplicative metric space. We consider the pair of non-self mappings X: P → G and Z: P → G and the mappings do not necessarily have a common fixed-point. In a complete fuzzy multiplicative metric space, if φ satisfy the condition φ (b, Zb, ς) = φ (P,G, ς) = φ (b, Xb, ς), then b is a common best proximity point. Further, we obtain the common best proximity point for the real valued functions L,M: (0, 1] → R by using a generalized fuzzy multiplicative metric space in the setting of (L,M)- iterative mappings. Furthermore, we utilize fuzzy multiplicative versions of the (L,M)-proximal contraction, (L,M)-interpolative Reich-Rus-Ciric type proximal contractions, (L,M)-Kannan type proximal contraction and (L,M)-interpolative Hardy-Rogers type proximal contraction to examine the common best proximity points in fuzzy multiplicative metric space. Moreover, we provide differential non-trivial examples to support our results. [ABSTRACT FROM AUTHOR]

This paper combines the concept of an arbitrary binary connection with the widely recognized principle of θ-contraction to investigate the innovative features of vector-valued metric spaces. This methodology demonstrates the existence of fixed points for both single- and multi-valued mappings within complete vector-valued metric spaces. Through the utilization of binary relations and θ-contraction, this study advances and refines the Perov-type fixed-point results in the literature. Furthermore, this article furnishes examples to substantiate the validity of the presented results. Additionally, we establish an application for finding the existence of solutions to a system of matrix equations.

In this paper, we prove fixed point theorem for a contractive map-ping which satisfy property P in Gb-metric space. Our results are supported by an example. [ABSTRACT FROM AUTHOR]

We establish fixed point theorems for nonlinear contractions on a metric space (not essentially complete) endowed with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those contained in Samet and Turinici [Commun. Math. Anal. 13, 82-97 (2012)] and Alam and Imdad [J. Fixed Point Theory Appl. 17(4), 693-702 (2015)]. Interestingly a corollary to one of our main results proved under symmetric closure of any binary relation remains a sharpened version of a theorem due to Samet and Turinici. Finally, we use examples to highlight the realized improvements in the results proved in this paper. [ABSTRACT FROM AUTHOR]

This paper consist of some generalized fixed point theorems in partial metric spaces. The concept of TF -contractive mappings are introduced in partial metric space and thus, a generalization of Banach's, Kannan's, Chatterjea's, Bianciari's fixed point theorems are established for concept of partial metric space. [ABSTRACT FROM AUTHOR]

In order to solve issues that arise in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization issues, equilibrium problems, complementarity issues, selection and matching problems, and issues proving the existence of solutions to integral and differential equations, fixed point theory provides vital tools. In this study, we discuss topological structure and several fixed-point theorems in the context of generalized neutrosophic cone metric spaces. In these spaces, the symmetric properties play an important role. We examine the existence and a uniqueness of a solution by utilizing new types of contraction mappings under some circumstances. We provide an example in which we show the existence and a uniqueness of a solution by utilizing our main result. These results are more generalized in the existing literature. [ABSTRACT FROM AUTHOR]

The ω -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified ω -distance mapping to introduce the notion of rational (α , β) φ - m ω contraction. We utilize our new notion to construct and formulate many fixed point results for a pair of two mappings defined on a nonempty set A. Our results modify many existing known results. In addition, we support our work by an example. [ABSTRACT FROM AUTHOR]

In this paper, we give three main theorems which are new generalizations of Banach fixed point theorem, Kannan fixed point theorem and Chatterjea fixed point theorem in the context of the ordered metric space. [ABSTRACT FROM AUTHOR]

The objective of this work is to study B-types of contraction mappings in the settings of partial metric space and establish fixed point results. As a result, a fixed point theorem has been established for a pair of B-type contraction mappings with a unique common fixed point. The study's main findings, in particular, expand and extend a fixed point theorem first proposed by Bijender et. al. in 2021. [ABSTRACT FROM AUTHOR]

Abstract In this paper, based on some geometrical properties of CAT p ( 0 ) $\operatorname{CAT}_{p}(0)$ spaces, for p ≥ 2 $p \geq 2$ , we obtain two fixed point results for monotone multivalued nonexpansive mappings and proximally monotone nonexpansive mappings. Which under some assumptions, reduce to coincide and generalize a fixed point result for monotone nonexpansive mappings. This work is a continuity of the previous work of Ran and Reurings, Nieto and Rodríguez-López done for monotone contraction mappings.

In this article, we introduce a new notion of ηcontraction and prove Widdle fixed point theorems, which provide a new generalization of the Banach contraction principle in different way than in the known results from the existing literature. Further, we include examples in support of our results. Finally, an application is presented which shows the existence and uniqueness of a solution for a class of Volterra type integral equations of the second kind. [ABSTRACT FROM AUTHOR]

In this paper, we provide sufficient conditions for the existence of fixed points for multivalued (α, ψ)-rational type contractive mappings in the setting of metric spaces. As applications, we derive a fixed point theorem for such class of contractions whenever the space is endowed with a graph. Several interesting corollaries are also deduced. The proved results generalize and extend various well-known results in the literature. [ABSTRACT FROM AUTHOR]

The ω -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified ω -distance mapping to introduce the notion of rational ( α , β ) φ - m ω contraction. We utilize our new notion to construct and formulate many fixed point results for a pair of two mappings defined on a nonempty set A. Our results modify many existing known results. In addition, we support our work by an example.

There have been numerous attempts recently to extend many of the metric standard fixed point theorems to a more general semimetric context. In many instances a weakened form of the triangle inequality is involved and the space is assumed to be complete. Thus Cauchy sequences play a central role. One of the standard tests to determine when a sequence is Cauchy in a metric space ( X, d) is the summation criterion: If $${\{ p_{n} \} \subset X}$$ and $${{\sum_{i=1}^{\infty}} d(p_{i}, p_{i+1}) < \infty}$$ , then { p} is Cauchy. In this note we examine instances in which this criterion plays a critical role. [ABSTRACT FROM AUTHOR]

The aim of this work is to develop a fuller theory regarding the existence, uniqueness and approximation of solutions to third-order boundary value problems via fixed point methods. To develop this deeper understanding of qualitative properties of solutions, our strategy involves an analysis of the problem under consideration, and its associated operator equations, within closed and bounded sets. This enables our new results to apply to a wider range of problems than those covered in the recent literature and we discuss several examples to illustrate the nature of these advancements. [ABSTRACT FROM AUTHOR]