Contraction Type Research Articles

Paired contractive mappings and fixed point results

<abstract><p>In this study, we explored a novel type of contraction, known as paired contraction (PC), to establish fixed points in metric spaces. It has been demonstrated that mappings possessing the PC property are continuous. We have also provided proofs for the existence of fixed points for such mappings with the classical Banach fixed point theorem emerging as a corollary. Furthermore, we presented examples of mappings that do not satisfy the standard contraction condition, but do exhibit the PC property.</p></abstract>

Fixed point for an $ \mathbb{O}g\mathfrak{F} $-c in $ \mathbb{O} $-complete $ \mathfrak{b} $-metric-like spaces

<abstract><p>In this article, we present the concepts of $ \mathbb{O} $-generalized $ \mathfrak{F} $-contraction of type-$ (1) $, type-$ (2) $ and prove several fixed point theorems for a self mapping in $ \mathfrak{b} $- metric-like space. The proved results generalize and extend some of the well known results in the literature. An example to support our result is presented. As an application of our results, we demonstrate the existence of a unique solution to an integral equation.</p></abstract>

On some contractive mappings and a new version of implicit function theorem in topological spaces

Study on existence of fixed points of contraction and contractive (type) mappings in topological spaces is a challenging task. The main goal of this article is to deal with this challenging task. To achieve our goal, we define two new contractive type mappings, namely, h-A-contractive and h-A1-contractive mappings on a topological space X, where h : X ? X ? R+ is a function and A, A1 are two collections of implicit functions. Then, we obtain some fixed point results concerning such contractive type mappings. Finally, as an application of one of the above mentioned fixed point results, we obtain a newer version of the implicit function theorem in topological spaces.

Fixed-point results via $ \alpha_{i}^{j} $-$ \left({\bf D}_{{\mathscr{C}}}\left(\mathfrak{P}_{\hat E}\right)\right) $-contractions in partial $ \flat $-metric spaces

<abstract><p>In this study, we characterize a novel contraction mapping referred to as $ \alpha_{i}^{j} $-$ \left({\bf D}_{{\mathscr{C}}}\left(\mathfrak{P}_{\hat E}\right)\right) $-contraction in light of $ {\bf D}_{\mathscr{C}} $-contraction mappings associated with the Geraghty-type contraction and $ E $-type contraction. Besides, a novel common fixed-point theorem providing such mappings is demonstrated in the context of partial $ \flat $-metric spaces. It is stated that the main theorem is a generalization of the existing literature, and its comparisons with the results are expressed. Additionally, the efficiency of the result of this study is demonstrated through some examples and an application to homotopy theory.</p></abstract>

Some fixed point results based on contractions of new types for extended $ b $-metric spaces

<abstract><p>The construction of contraction conditions plays an important role in science for formulating new findings in fixed point theories of mappings under a set of specific conditions. The aim of this work is to take advantage of the idea of extended $ b $-metric spaces in the sense introduced by Kamran et al. [A generalization of $ b $-metric space and some fixed point theorems, <italic>Mathematics</italic>, <bold>5</bold> (2017), 1–7] to construct new contraction conditions to obtain new results related to fixed points. Our results enrich and extend some known results from $ b $-metric spaces to extended b-metric spaces. We construct some examples to show the usefulness of our results. Also, we provide some applications to support our results.</p></abstract>

Some fixed point results for fuzzy generalizations of Nadler's contraction in b-metric spaces

<abstract> <p>The main purpose of this study is to examine the existence of fuzzy fixed points of fuzzy mappings meeting the criteria of some generalized contractions of Nadler's type in the framework of complete b-metric spaces. From the pertinent literature, there are additional previous observations that are provided as corollaries. Our study expands and incorporates several implications that are apparent in this mode and are addressed in considerable literature.</p> </abstract>

Fixed point theorems of enriched Ciric's type and enriched Hardy-Rogers contractions

Fixed point theorems of enriched Ciric's type and enriched Hardy-Rogers contractions

A novel approach of multi-valued contraction results on cone metric spaces with an application

<abstract><p>In this paper, we present some generalized multi-valued contraction results on cone metric spaces. We use some maximum and sum types of contractions for a pair of multi-valued mappings to prove some common fixed point theorems on cone metric spaces without the condition of normality. We present an illustrative example for multi-valued contraction mappings to support our work. Moreover, we present a supportive application of nonlinear integral equations to validate our work. This new theory, can be modified in different directions for multi-valued mappings to prove fixed point, common fixed point and coincidence point results in the context of different types of metric spaces with the application of different types of integral equations.</p></abstract>

Fixed point theorem via measure of non-compactness for a new kind of contractions

In this paper, we will use the notion of α-admissible mappings in Banach spaces, to introduce the concept of Tβ-contractive mappings and establish a fixed point theorem for this type of contractions. Our theorems generalize and improve many results in the literature. Moreover, we apply the main result to prove the existence of a solution for Volterra-integral equation, under more general assumptions than previously made.

Fixed point theorems for $ (\alpha, \psi) $-rational type contractions in Jleli-Samet generalized metric spaces

<abstract><p>The aim of this article is to present some results regarding $ (\alpha, \psi) $-rational type contractions in the setting of the generalized metric spaces introduced by Jleli and Samet. By the nature of these types of contractions which use also comparison functions, new fixed point theorems are established. Already known facts appear as consequences of our outcomes. Examples and comments point out the applicability of our approach.</p></abstract>

Fixed and coincidence point theorems on partial metric spaces with an application

The aim of this paper is to investigate some fixed and co-incidence point theorems in complete, orbitally complete and (T, f)-orbitally complete partial metric spaces under the generalized contractive type conditions of mappings. Moreover, our results generalize and extend the several obtained results in the literature. Additionally some non-trivial examples are demonstrated, and an application has discussed to integral equations.

ON COMPLEX VALUED FUZZY b - METRIC SPACE

In this paper, the notion of complex-valued fuzzy b-metric space is introduced. In this newly developed structure, we have established a sucient condition for a sequence to be Cauchy. Moreover, under suitable conditions of contractive type, the existence and uniqueness of fixed points of self-maps are established in this structure. To demonstrate the validity of the hypothesis and the degree of generality of our results, some examples are also furnished.

Fixed point theorems for self mappings in generalized metric spaces

In this paper a fixed point theorem in D- metric space using contractive type mappings is discussed. This work is an extension of the result obtained in [2].

Towards coupled coincidence theorems of generalized admissible types of mappings on partial satisfactory cone metric spaces and some applications

<abstract><p>This paper introduces a novel class of generalized $ {\alpha} $-admissible contraction types of mappings in the framework of $ {\theta} $-complete partial satisfactory cone metric spaces and proves the existence and uniqueness of coincidence points for such mappings. In this setting, the topology generated and induced by the partial satisfactory cone metric is associated with semi-interior points rather than interior points of the underlying cone. In addition, some applications of the paper's main coincidence point theorems are given. The results of this paper unify, extend and generalize some previously proved theorems in this generalized setting.</p></abstract>

FIXED POINT RESULTS FOR MULTI-VALUED GRAPH CONTRACTIONS ON A SET ENDOWED WITH TWO METRICS

In this paper we will study existence, uniqueness and data depen­dence of the fixed points of multi-valued operators on a set endowed with two metrics. The case of multi-valued graph contractions is con­sidered. Then, an extension to a more general contraction type condi­tion is also given.

Some fixed point results for nonlinear contractive conditions in ordered proximity spaces with an application

<abstract><p>In this article, we use the concept of proximity spaces to prove common fixed point results for mappings satisfying generalized ($ \psi $, $ \beta $)-Geraghty contraction type mapping in partially ordered proximity spaces. Finally, we investigate an application to endorse our results.</p></abstract>

Some approximate fixed point results for various contraction type mappings

Some approximate fixed point results for various contraction type mappings

Fixed-points of interpolative Kannan type contractions in bipolar metric spaces

Fixed-points of interpolative Kannan type contractions in bipolar metric spaces

Chatterjea type theorems for complex valued extended $ b $-metric spaces with applications

<abstract><p>In this article, we establish common $ \alpha $ -fuzzy fixed point theorems for Chatterjea type contractions involving rational expression in complex valued extended $ b $-metric space. Our results generalize and extend some familiar results in the literature. Some common fixed point results for multivalued and single valued mappings are derived for complex valued extended $ b $-metric space, complex valued $ b $-metric space and complex valued metric space as consequences of our leading results. As an application, we investigate the solution of Fredholm integral inclusion.</p></abstract>

On a common fixed point theorem in vector-valued $ b $-metric spaces: Its consequences and application

<abstract><p>We introduce a Ćirić type contraction principle in a vector-valued $ b $-metric space that generalizes Perov's contraction principle. We investigate the possible conditions on the mappings $ W, E:G\rightarrow G $ ($ G $ is a non-empty set), for which these mappings admit a unique common fixed point in $ G $ subject to a nonlinear operator $ {\bf F}:\mathbb{P}^{m} \rightarrow \mathbb{R}^{m} $. We illustrate the hypothesis of our findings with examples. We consider an infectious disease model represented by the system of delay integro-differential equations and apply the obtained fixed point theorem to show the existence of a solution to this model.</p></abstract>