Contraction Type Research Articles

A fixed point principle in ordered metric spaces and applications to rational type contractions

<abstract><p>Fixed points results for rational type contractions in metric spaces have been widely studied in the literature. In the last years, many of these results are obtained in the context of partially ordered metric spaces. In this paper, we introduce a fixed point principle for a class of mappings between partially ordered metric spaces that we call orbitally order continuous. We show that the hypotheses in the statement of such a principle are not redundant and, in addition, that they cannot be weakened in order to guarantee the existence of a fixed point. Moreover, the relationship between this kind of mappings and those that are continuous and orbitally continuous is discussed. As an application, we extend many fixed point theorems for continuous contractions of rational type to the framework of those that are only orbitally order continuous. Furthermore, we get extensions of the aforementioned metric fixed point results to the framework of partial metrics. This is achieved thanks to the fact that each partial metric induces in a natural way a metric in such a way that our new principle is applicable. In both approaches, the metric and the partial metric, we show that there are orbitally order continuous mappings that satisfy all assumptions in our new fixed point principle but that they are not contractions of rational type. The explored theory is illustrated by means of appropriate examples.</p></abstract>

Fixed point results for nonlinear contractions of Perov type in abstract metric spaces with applications

<abstract><p>In this paper, we present some common fixed point results for $ g $-quasi-contractions of Perov type in cone $ b $-metric spaces without the assumption of continuity. Besides, by constructing a non-expansive mapping from a real Banach algebra $ \mathcal{A} $ to $ \mathcal{B}(\mathcal{A}) $, the space of all of its bounded linear operators, we explore the relationship between the results for the mappings of Perov type on cone metric (cone $ b $-metric) spaces and that for the corresponding mappings on cone metric (cone $ b $-metric) spaces over Banach algebras. As consequences, without the assumption of normality, we obtain common fixed point theorems for generalized $ g $-quasi-contractions with the spectral radius $ r(\lambda) $ of the $ g $-quasi-contractive constant vector $ \lambda $ satisfying $ r(\lambda)\in [0, \frac{1}{s}) $ (where $ s\ge 1 $) in the setting of cone $ b $-metric spaces over Banach algebras. In addition, we also get some fixed point theorems for nonlinear contractions of Perov type in the setting of cone normed spaces. The main results generalize, extend and unify several well-known comparable results in the literature. Finally, we apply our main results to some nonlinear equations.</p></abstract>

Double controlled $ M $-metric spaces and some fixed point results

<abstract><p>In this article, we introduce the idea of double controlled $ M $-metric space by employing two control functions $ a(u, w) $ and $ \beta (w, v) $ on the right-hand side of the triangle inequality of $ M $-metric space. We provide some examples of double controlled $ M $-metric spaces. We also provide some fixed point results under new type of contractions in the setting of double controlled $ M $-metric spaces. Moreover, we give an example to highlight the importance of one of our main results.</p></abstract>

Neuromuscular and functional responses to concentric and eccentric strength training in older adults

The type of muscle action is important when designing exercise interventions for older individuals and may result in different effects. In this study we performed a systematic review of controlled trials comparing the effects of concentric and eccentric resistance training, performed on isokinetic dynamometers, on lower extremity muscular and functional performance in older adults (CDR42017075316). Six databases (Pubmed, CINAHL, SPORTDiscus, PEDro, Cochrane Central and Embase) were searched. Outcomes of interest concerned neuromuscular and functional performance. Trials should consider 65 years or older individuals participating in concentric and/or eccentric training on isokinetic dynamometers, at least twice a week, during at least four weeks. Results should be compared to a control group or between different contraction types. A qualitative analysis of data was done. Quality assessment considered the Cochrane Risk of Bias Tool. The initial search returned 10376 studies and four trials were considered for inclusion. Three trials compared the effects of concentric training with the ones of control groups, and one compared the effects of concentric with the ones of eccentric training. All trials focused on knee extensor and flexor muscles, and one also focused on ankle dorsiflexors and plantarflexors. Training programs included three sessions/week lasting 8-12 weeks. Concentric training improved strength, power, and muscle antagonist coactivation compared to the control. Concentric and eccentric training improved knee isometric, concentric and eccentric strength and self-paced step test, with no effect on gait speed. They did not consider muscle structural parameters. The findings of beneficial effects of isokinetic concentric and eccentric resistance training on muscle strength and power in older adults were consistent. However, there is a lack of trials addressing the effects of isokinetic strength training on muscle structure and functionality.

Discussion on the hybrid Jaggi-Meir-Keeler type contractions

<abstract><p>In this paper, the notion of hybrid Jaggi-Meir-Keeler type contraction is introduced. The existence of a fixed point for such operators is investigated. The derived results combine and extend a number of existing results in the corresponding literature. Examples are established to express the validity of the obtained results.</p></abstract>

C ∗‐Algebra‐Valued Extended Rectangular Hb‐Metric Spaces and Presić‐Type Fixed Point Theorem with an Application

In this article, we introduce the concept of C ∗‐algebra‐valued extended rectangular Hb‐metric spaces and use it to prove the Banach contraction principle (BCP). Also, we extend this concept to Presić type contractions and use a method to shorten the proof. We also take an application to show the usefulness of our main result.

Interpolative Hardy Roger's type contraction on a closed ball in ordered dislocated metric spaces and some results

<abstract><p>The aim of this paper is to find out fixed point results with interpolative contractive conditions for pairs of generalized locally dominated mappings on closed balls in ordered dislocated metric spaces. We have explained our main result with an example. Our results generalize the result of Karapınar et al. (Symmetry 2018, 11, 8).</p></abstract>

A note on three different contractions in partially ordered complex valued $ G_b $-metric spaces

<abstract><p>In this paper, we introduce the complex valued $ C^{p} $-class function, a type of Geraghty contraction and a type of JS contraction in complete partially ordered complex valued $ G_b $-metric spaces, prove three fixed point theorems in this space, and also we give some examples to support our results.</p></abstract>

On Almost Type α-F-Z-Weak Contraction in Metric Spaces

In this article, we introduce a new type of contraction named almost type α-F-Z-weak contraction, which comes from a combination of F-contraction, Z-contraction, and almost contraction, and then we provide sufficient conditions for the existence and uniqueness of fixed point of such contractions in complete metric spaces and give some related fixed point results. In addition, some related fixed point results can derive from our main results.

Some coupled fixed point theorems on multiplicative metric spaces with an application

<abstract><p>This article aims to prove some coupled fixed point (FP) theorems for nonlinear contractive type mapping in multiplicative metric space (MM-space). Our presented work consists of the maximum type and some other expressions in the framework of MM-space. We also provide illustrative examples and an application in support of our generalized results. Our offered results expand and develop a variety of the latest outcomes in the existing literature. Moreover, we present an application of the two Urysohn integral equations to support our work.</p></abstract>

On symmetric Meir-Keeler contraction type couplings with an application

Recently, a class of mappings named as couplings was introduced in [U.P.B. Sci. Bull. Series A, 79 (2017), 1-12]. Based on this concept, we introduce symmetric Meir-Keeler couplings and we ensure the existence of strong coupled fixed points. We present some concrete examples to support the obtained results. Furthermore, as an application of our results, we investigate the existence of a unique solution to a system of integral equations.

Solving an integral equation via orthogonal generalized $ {\boldsymbol{\alpha}} $-$ {\boldsymbol{\psi}} $-Geraghty contractions

<abstract><p>In this paper, we introduce orthogonal generalized $ {\bf{O}} $-$ {\boldsymbol{\alpha}} $-$ {\boldsymbol{\psi}} $-Geraghty contractive type mappings and prove some fixed point theorems in $ {\bf{O}} $-complete $ {\bf{O}} $-$ \mathfrak{b} $-metric spaces. We also provide an illustrative example to support our theorem. The results proved here will be utilized to show the existence of a solution to an integral equation as an application.</p></abstract>

Some Common Fixed Point Results in Cone Metric Spaces for Rational Contractions

A very engrossing technique in theory of contractive mapping fixed point. A number of authors have defined contractive type mappings on a cone metric spaces X which are generalization of the well -known Banach contraction, and have the property that each of such mapping has a unique fixed point. The fixed point can always be found by using Picard Iteration, opening with initial choice x₀∈X. In this manuscript, we generalize, extend and improve the result under the assumption of normality of cone for rational expression type contraction mapping in cone metric spaces. The present article is to provide a new alternative proof for two and three mapping and obtain the entity and exclusiveness of common fixed point. The concernment of the present paper to open a new direction of proof to be extended based on the methods of rational type contraction mapping in cone metric spaces of fixed-point theory. The assistance of this article is organized as follows. In section 2, preliminary notes. In this section we recall some standard notations and definitions which we needed. In section 3, the main results of the author are given. In this section we evidence of new results for two and three maps. In section 4, gives brief concluding note of the paper.

A unification of Geraghty type and Ciric type fixed point theorems

In the framework of metric spaces, we introduce the concept of Geraghty-Ciric type contractions and show the existence and uniqueness of the fixed point of such mappings. This result improves and unifies those obtained by Geraghty (Proc. Amer. Math. Soc. 40, 604-608 (1973)) and Ciric (Proc. Amer. Math. Soc. 45, 267-273, (1974)). Several technical lemmas are employed to ensure that a Picard sequence is a Cauchy sequence. In addition, two illustrative examples are provided to indicate the validity of the obtained results.

Some coupled coincidence and coupled common fixed point result in dislocated quasi b-metric spaces for rational type contraction mappings

The aim of this paper is to establish coupled coincidence and coupled common fixed point theorems involving a pair of weakly compatible mappings satisfying rational type contractive condition in the setting of dislocated quasi b-metric spaces. The presented result improves and generalizes several well-known comparable results in the existing literature. We also provided an example in support of our main result.

Common coupled fixed and coincidence points results for rational type contraction mappings in complex valued Sb-metric spaces

In this paper, we introduce a new rational type contraction mapping in complex valued Sb-metric space and find some common coupled fixed and coincidence points. Some results are also given as corollaries.

Fixed points for intimate mappings

In this paper, we introduce (ψ,φ)-weak contraction condition that involves cubic terms of distance function. We prove some fixed point theorems for pairs of intimate mappings satisfying newly introduced contraction condition and generalize the result of Murthy and Prasad [14] and Jain et al. [8]. At the end, an application for integral type contraction condition is given.

A geometric approach to the Proinov type contractions

In this paper, we prove some fixed-circle, fixed-disc and fixed-ellipse results on metric spaces. To do this, we define the notions of Proinov type a0-contraction and generalized Proinov type a0-contraction. Also, we give some illustrative examples to show the validity of our obtained results. Finally, we present a nice application to exponential linear unit activation functions.

Generalized a-min special type contraction results on 2-Menger spaces

The goal of this paper is to present some novel probabilistic a-minimum contraction results on probabilistic 2-metric spaces. Our findings are based on probabilistic 2-metric spaces, which are the probabilistic generalisations of 2-metric spaces. An illustrative example backs up our findings.

A Fixed Point Theorem Satisfying Integral Type Contraction in Revised Fuzzy Metric Space

In this paper, we analyze the existence of fixed points for mappings defined on a complete revised fuzzy metric space satisfying a contractive condition of integral type.