Point Theorems In Metric Spaces Research Articles

BEST PROXIMITY AND FIXED POINT OUTCOMES IN METRIC SPACES FOR THE PROXIMAL CONTRACTION OF α0−(ψ0,g0)

In this paper, we introduce new notions of α0−(ψ0,g0)- proximal contraction of Type-I and Type-II and modified α0 − (ψ0,g0)- proximal contraction. In the setting of these notions, we prove certain fixed point theorems in metric space. Additionally, a few applications are provided to show how the results can be used.

On metrization of fuzzy metrics and application to fixed point theory

It is a well-known fact that the topology induced by a fuzzy metric is metrizable. Nevertheless, the problem of how to obtain a classical metric from a fuzzy one in such a way that both induce the same topology is not solved completely. A new method to construct a classical metric from a fuzzy metric, whenever it is defined by means of an Archimedean t-norm, has recently been introduced in the literature. Motivated by this fact, we focus our efforts on such a method in this paper. We prove that the topology induced by a given fuzzy metric M and the topology induced by the metric constructed from M by means of such a method coincide. Besides, we prove that the completeness of the fuzzy metric space is equivalent to the completeness of the associated classical metric obtained by the aforementioned method. Moreover, such results are applied to obtain fuzzy versions of two well-known classical fixed point theorems in metric spaces, one due to Matkowski and the other one proved by Meir and Keeler. Although such theorems have already been adapted to the fuzzy context in the literature, we show an inconvenience on their applicability which motivates the introduction of these two new fuzzy versions.

Fixed Point Theorems Using α-Admissible Mappings in Metric Spaces

In this paper, we shall prove the fixed point theorems in metric space using \(\alpha\) - admissible mapping. Some existing results of literature shall be deduced from the main results. In the end, we shall provide an example to support our result.

An elementary best proximity point theorem in metric spaces

An elementary best proximity point theorem in metric spaces

Caristi’s Fixed Point Theorem in <i>G</i>-Cone Metric Spaces and Application

In this work, we introduce a few versions of Caristi’s fixed point theorems in G-cone metric spaces which extend Caristi’s fixed point theorems in metric spaces. Analogues of such fixed point theorems are proved in this space. Our work extends a good number of results in this area of research.

Common Fixed Point Theorems on Compatibility and Continuity in Soft Metric Spaces

In this paper, basic notions of soft sets are introduced and some important properties of soft metric spaces are established. It is shown that soft metric extensions of several important fixed point theorems for metric spaces can be directly deduce from comparable existing results. Some examples are given to validate and illustrate the approach. Obtained results modify, improve, sharpen, enrich and generalize various known results.

Common Fixed Point Theorems via Inverse C k − Class Functions in Metric Spaces

In this paper, we firstly introduce a new notion of inverse C k − class functions which extends the notion of inverse C − class functions introduced by Saleem et al., 2018. Secondly, some common fixed point theorems are stated under some compatible conditions such as weak semicompatible of type A , weak semicompatibility, and conditional semicompatibility in metric spaces. Moreover, we introduce a new kind of compatibility called S τ − compatibility which is weaker than E . A . property and also present a common fixed point theorem in metric spaces via inverse C k − class functions. Some examples are provided to support our results.

Binary relation for tripled fixed point theorem in metric spaces

In this paper we present a new extension of tripled fixed point theorems in metric spaces endowed with a reflexive binary relation that is not necessarily neither transitive nor antisymmetric. The key feature in this tripled fixed point theorems is that the contractivity condition on the nonlinear map is only assumed to hold on elements that are comparable in the binary relation. Next on the basis of the tripled fixed point theorems, we prove the existence and uniqueness of positive definite solutions of a nonlinear matrix equation of type

Some common best proximity point theorems via a fixed point theorem in metric spaces

Some common best proximity point theorems via a fixed point theorem in metric spaces

Functional-Type Caristi–Kirk Theorem on Menger Space and Application

In this paper, we extend Caristi’s fixed point theorem in metric spaces to probabilistic metric spaces, and also, we prove some common fixed point theorems for a pair of mappings satisfying a system of Caristi-type contractions in the setting of a Menger space. Two examples are given to support the main results. Furthermore, we have functional equations as an application for the main theorem.

Generalized contractions for a sequence of multi-valued mappings

The aim of this paper is to obtain a general result for existence of common fixed points for a sequence of multi-valued mappings on a K-quasimetric space endowed with a graph. This will enable us to present a simultaneous generalization of various types of fixed point theorems in the literature. In particular, we show that some fixed point theorems in metric spaces can be generalized to 2-quasimetric spaces.. We also provided an example to show that our results are genuine generalization of some old results.

On Caristi’s fixed point theorem in metric spaces with a graph

We generalize the Caristi’s fixed point theorem for single valued as well as multivalued mappings defined on ametric space endowed with a graph andw-distance. Particularly, we modify the concept of the (OSC)-propertydue to Alfuraidan and Khamsi (Alfuraidan M. R. and Khamsi, M. A.,Caristi fixed point theorem in metric spaceswith graph, Abstr. Appl. Anal., (2014) Art. ID 303484, 5.) which enable us to reformulated their stated graphtheory version theorem (Theorem 3.2 in Alfuraidan M. R. and Khamsi, M. A.,Caristi fixed point theorem in metricspaces with graph, Abstr. Appl. Anal., (2014) Art. ID 303484, 5. ) to the case ofw-distance. Consequently,we extend and improve some recent works concerning extension of Banach Contraction Theorem tow-distancewith graph e.g. (Jachymski, J.,The contraction principle for mappings on a metric space with graph, Proc. Amer. Math.Soc.,136(2008), No. 4, 1359–1373; Nieto, J. J., Pouso, R. L. and Rodriguez-Lopez R.,Fixed point theorems in orderedabstract spaces, Proc. Amer. Math. Soc.,135(2007), 2505–2517 and Petrusel, A. and Rus, I.,Fixed point theorems inorderedL−spaces endowed with graph, Proc. Amer, Math. Soc.,134(2006), 411–418.

Common fixed point theorem for mapping with the generalized weakly contractive conditions in metric spaces

In this paper, we discuss the existence and uniqueness of fixed point and common fixed point theorems in metric spaces by introducing a generalized weakly contractive mapping, which generalize and unify some well known results in the literature.

Common fixed point theorems in metric space using new CLR property

In this paper we present a new class of functions called Weakly CLR*_\( (f,g),T\) property which generalizes the class of mappings already defi ned in the literatures [8]. We obtain a result on Common fi xed point theorem in metric space for mappings satisfying weakly CLR*_\( (f,g),T\) property. Some examples to justify our results are given.

Some ϕ-fixed point results in b-metric spaces with applications

The fixed point theory is the most important topic in mathematics anaysis. This topic has many applications in the different fields. It demonstrates the uniqueness of the existence of a mapping and how it can be found. The Banach contraction mapping principle is most important theorem in the fixed point theory. Most authors have introduced new contractions and they proved some fixed point theorems in metric spaces. On the other hand, some authors introduced new metric spaces as a generalization of metric spaces. Later, they proved fixed point theorems which generalize the Banach contraction principle for various mappings in several metric spaces. The purpose of this study is to introduce the existence and uniqueness of ϕ-fixed point for some new contractions in complete b-metric spaces. Firstly, we presented new definitions called (F,ϕ,α,θ)_{s} and (F,ϕ,α,θ)_{s}-weak contractions in complete b-metric spaces as a generalization of metric spaces. Later, we proved ϕ-fixed point theorems for (F,ϕ,α,θ)_{s} and (F,ϕ,α,θ)_{s}-weak contractions in complete b-metric spaces. The presented theorems extend and generalize some ϕ-fixed point results which are known in the literature. As applications, we derived some fixed point results in complete partial b-metric spaces as a generalization of partial metric spaces. The results in this paper generalizes may existing results in the literature.

On algebraic properties of soft real points

In this paper, we introduce and discuss soft single points, which proceed towards soft real points by using real numbers and subsets of set of real numbers. We also define the basic operations on soft real points and explore the algebraic properties. We observe that the set of all soft real points forms a ring. Moreover, we study the soft real point metric using soft real point and explore some of its properties. We then establish a soft real point contraction fixed point theorem using soft real point metric space. It is interesting to mention that these concepts may be helpful for researchers to navigate the ideas put forth in a soft metric extension of several important fixed point theorems for metric spaces deduced from comparable existing results.

Hybrid Coupled Fixed Point Theorems in Metric Spaces with Applications

In this manuscript, using CLR property, coupled coincidence and common coupled fixed point results for two-hybrid pairs satisfying (F,φ)- contraction are demonstrated. Using the established results existence of solution to the coupled system of functional and nonlinear matrix equations is also discussed. We provide examples where the main theorem is applicable but most current relevant results in literature fail to have a common coupled fixed point.

Best Proximity Point Theorems in Metric Spaces

Best Proximity Point Theorems in Metric Spaces

A new type of α − F− contraction on common fixed point theorems in metric spaces and its application

A new type of α − F− contraction on common fixed point theorems in metric spaces and its application

Kantorovich’s Fixed Point Theorem in Metric Spaces and Coincidence Points

Existence and uniqueness theorems are obtained for a fixed point of a mapping from a complete metric space to itself. These theorems generalize the theorems of L. V. Kantorovich for smooth mappings of Banach spaces. The results are extended to the coincidence points of both ordinary and set-valued mappings acting in metric spaces.