Contractive Condition Research Articles

Results pertaining to fixed points in ordered metric spaces with auxiliary functions and application to integral equation

<abstract><p>This paper delves into fixed point findings within a complete partially ordered $ b $-metric space, focusing on mappings that adhere to weakly contractive conditions in the presence of essential topological characteristics. These findings represent modifications of established results and further extend analogous outcomes in the existing literature. The conclusions are substantiated by illustrative examples that strengthen the conclusion of the paper.</p></abstract>

New fixed point theorems in dynamic property under rational contractive condition with application

New fixed point theorems in dynamic property under rational contractive condition with application

Solving nonlinear matrix and Riesz-Caputo fractional differential equations via fixed point theory in partial metric spaces

A modified implicit relation and ?-implicit contractive condition are introduced in the setting of relational partial metric spaces and some related fixed point results are derived. Two suitable examples are provided. As an application, sufficient conditions are derived for the existence of a unique positive definite solution of the non-linear matrix equation X = B + Pk i=1A* i T(X)Ai. An example is given, using matrices that are randomly generated, as well as convergence and error analysis and average CPU time analysis. Solving fractional differential equations of Riesz-Caputo type with anti-periodic boundary conditions is also discussed, followed by two illustrations.

RATIONAL TYPE INTUITIONISTIC FUZZY CONTRACTION RESULTS IN INTUITIONISTIC FUZZY METRIC SPACES WITH AN APPLICATION

The purpose of this study is to propose a new idea of rational type intuitionistic fuzzy contraction mappings in intuitionistic fuzzy metric spaces. We show several fixed point results in intuitionistic fuzzy metric spaces under rational type intuitionistic fuzzy contraction conditions, with detailed examples to back up our claims. This revolutionary idea will be crucial in the theory of intuitionistic fuzzy fixed point outcomes and can be applied to other contractive type mappings in the setting of intuitionistic fuzzy metric spaces. Furthermore, to support our work, we offer an application of a nonlinear integral type problem to obtain the current result for a unique solution.

Convergence results for cyclic-orbital contraction in a more generalized setting with application

<abstract><p>In the realm of double-controlled metric-type spaces, we investigated obtaining fixed points using the application of cyclic orbital contractive conditions. Diverging from conventional approaches utilized in standard metric spaces, our technique took a unique route due to the unique features of our structure. We demonstrated the significance of our outcomes through exemplary cases, clarifying the breadth of our results through comprehensive investigations. Significantly, our work not only improved and broadened earlier findings in the literature, but also offered unique notions that were discussed in our explanatory notes. Towards the end of our inquiry, we used insights obtained from previous discoveries to develop a second-order differential equation. This equation was an effective tool for dealing with the second class of Fredholm integral problems. In conclusion, this investigation extended our examination of double-controlled metric type spaces by providing new insights on fixed point theory, expanding on prior debates and building a substantial road towards solving a class of integral equations.</p></abstract>

COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN MULTIPLICATIVE CONE METRIC SPACE

In this article, we first introduce the idea of weakly compatible mappings in multiplicative cone metric space and then prove some common fixed point theorems for two pairs of weakly compatible mappings that satisfy a contractive condition in multiplicative cone metric space with a multiplicative normal cone setting. Examples are also provided to support our findings.

Convergence : Partially ordered soft topological space

This research paper introduce Symmetrical and sequentially dense soft set and isometry in the context of POS topological space. Inspired by Matthew’s seminal work on dataflow network research, we extend the study to soft universe, bridging classical metrics with soft computing to represent imprecision in complex systems. We investigate sequence convergence in partial soft topological spaces, revealing essential insights and contributing to our understanding of partial soft metrics. Additionally, we introduce the idea of Convergence of partially ordered soft topological spaces along with we provide examples to support the obtained results and relations. In the future, these results can be further applied to analyze and understand the properties and convergence of soft topological spaces with the contraction condition for soft fixed point theory.

O nekim rezultatima fiksne tačke za ekspanzivna preslikavanja u S-metričkim prostorima

Introduction/purpose: The aim of this paper is to establish some existence results of a fixed point for a class of expansive mappings defined on a complete S-metric space. Methods: An iteration scheme was used. Results: Some existing results of mappings satisfying contractive conditions are expanded to expansive ones, providing a new condition expressed in one variable under which the existence of a fixed point holds. Conclusions: This work provides new tools to fixed point theory together with their applications.

FIXED POINT RESULT USING TWO DOMINATED MAPPING ON A CLOSED BALL

In the present work, we obtain the result of fixed-point theorem through quasi-contraction mapping and improve the work of A. Shoaib et.al (2015) in a left and right K-sequentially 0-complete ordered quasi-partial spaces respectively, where locally contractive condition satisfied on a closed set. We can use this result to solve the complication of computer algorithms and study it. In this paper, some fixed-point results of self-mapping which is defined on quasi partial metric spaces are given by using dominated mapping (A. Shoaib et.al, 2015) in a left and right K-sequentially 0-complete ordered quasi-partial spaces respectively. Where locally contractive condition satisfied on a closed set. And by taking advantage of these results, the necessary conditions for self-mappings on quasi partial metric spaces in quasi contraction are investigated and prove existence and uniqueness theorem of fixed point for contraction mapping. We can use this result to solve the complication of computer algorithms and study it.

FIXED POINT RESULTS FOR THREE MAPPINGS USING CONTRACTIVE CONDITIONS IN TVS-VALUED CONE METRIC SPACE

In this article, we prove fixed point theorems using c-distances for three mappings in tvs-valued cone metric space under contractive conditions. The results obtained in this paper generalize and extend the results presented in the literature. Some examples are presented to validate our obtained results.

AN APPROACH TO THE STUDY OF FIXED POINT THEORY IN HILBERT SPACE

The purpose of this article is to extend Banach’s contraction principle through a new rational expression in the contractive condition to establish the existence and uniqueness of fixed point of a closed subset of Hilbert space to a self mapping. The result is extended to a pair of self mappings and positive integers powers of a pair mapping and further extended to a sequence of mappings in the space. The presented results extend and generalized various known comparable results from the current literature.

Muscle Fiber Conduction Velocity During Electrically Stimulated Contraction at Various Joint Angles, During Joint Movements, and During Voluntary Contractions.

Muscle fiber conduction velocity (MFCV) can be affected by muscle fiber geometry at different joint angles and during joint movements. This study aimed to investigate MFCV during electrically evoked contraction at different joint angles, during joint movements, and during voluntary contractions. Sixteen healthy young men participated. A stimulation electrode was attached on the innervation zone of the vastus lateralis, and a linear electrode array was attached on the vastus lateralis. Under a static condition, electrically evoked electromyography signals were recorded at knee joint angles set every 15° between 0° and 105°. Under a passive movement condition, signals were recorded during knee extension and flexion passively. Under a voluntary contraction condition, signals were recorded while performing 30% or 60% of maximum voluntary contraction. MFCV was calculated using cross-correlation coefficients. Under the static condition, there were no differences in MFCV among various joint angles. Under the passive movement condition, MFCV was significantly greater during high velocity or shortening. Under the voluntary contraction condition, MFCV was significantly greater during high-intensity voluntary contraction and with a shortened muscle length. Joint angles do not influence MFCV markedly during relaxation, but it is possible to overestimate MFCV during movement or voluntary contraction.

Generalized almost Contractions on Extended Quasi-Cone B-Metric Spaces

Fixed Point Theory is among the most valued research topics nowadays. Over the years, it has been developed in three directions: by generalizing the metric space, by establishing new contractive conditions, and by applying its results to various fields such as Differential Equations, Integral Equations, Economics, etc. In this paper, we define a new class of cone metric spaces called the class of extended quasi-cone b-metric spaces. Extended quasi-cone b-metric spaces generalize cone metric spaces and quasi-cone b-metric spaces. We have studied topological issues, such as the right and left topologies, right (left) Cauchy, and convergent sequences. Furthermore, there are determined generalized τ-almost contractions, which extend the almost contractions. The highlight of this study is the investigation of the existence and uniqueness of a fixed point for some types of generalized τ-almost contractions in extended quasi-cone b-metric space. We prove some corollaries and theorems for known contractions in extended quasi-cone b-metric spaces. Our results generalize some known theorems given in literature due to the new cone metric spaces and contractions. Concrete examples illustrate theoretical outcomes. In addition, we show an application of the main results to Integral Equations, which provides the applicative side of them.

Reducing residual stress in photopolymerized composites by grafting high-mobility polymer chains onto the filler-matrix interface

3D/4D printing of thermosets, composites and hydrogels, lithographic procedures and dental resins are important examples of applications that rely on light-driven polymerization supported on substrates. Adhesion between the polymer and substrate during photopolymerization (and even between printed layers) can restrict the usual polymerization shrinkage, leading to the generation of residual stresses. These residual stresses can result in poor-quality products due to the presence of cracks and occurrence of warpage. In this work, silica nanoparticles were incorporated into photopolymerizable dimethacrylate based networks. These nanoparticles had their surface modified by grafting polymer chains with high mobility at usual room temperatures (low glass transition temperature polymer) and with high affinity towards the polymer matrix in order to test the hypothesis that these high-mobility chains could be helpful in dissipating stress and energy generated during photopolymerization in conditions in which the polymerization shrinkage is restricted. The nanoparticles and composites were analyzed via: electron microscopy (SEM), thermal analysis and mechanical bending tests. The evolution of the monomer-to-polymer conversion during photopolymerization was monitored using real-time infrared (FTIR) spectroscopy. To determine the residual stress generated by the polymerization at restricted contraction conditions, a universal mechanical testing machine was adapted and used. The results showed that silica nanoparticles with grafted high-mobility polymer chains that were able to interpenetrate and interact with the dimethacrylate based networks led to the production of composites having higher mechanical properties and lower polymerization stresses than composites containing only silanized nanoparticles and nanoparticles having immiscible polymer grafts towards the dimethacrylate based network. Results indicate that the modifications of the interface of composites developed in this work can be useful in the formulation of materials with improved mechanical properties and stability regarding polymerization shrinkage and residual stress that can lead to higher-quality products obtained in processes that employ light-driven polymerization supported on substrates or that occur on sequential polymerized layers, such as 3D/4D printing, lithography and in dental applications.

Convergence results based on graph-Reich contraction in fuzzy metric spaces with application

This article introduces a novel class of Reich-type contractions that meet the graph preservation criteria in the context of complete fuzzy metric spaces. The provided contraction condition is satisfied through various forms of contractive mappings via directed graphs in the literature. Our key result is the natural extension of fuzzy metric spaces to fuzzy metrics enriched with a graph, which adds the understanding of fixed points in metric spaces within the realm of graph structure. The findings are further supported by examples and applications.

Exploring Integral ϝ-Contractions with Applications to Integral Equations and Fractional BVPs

In this article, two types of contractive conditions are introduced, namely extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction. For the case of two mappings and their coincidence point theorems, a variant of (ϰ,Ω-Ϝ)-contraction has been introduced, which is called (ϰ,Γ1,2,Ω-Ϝ)-contraction. In the end, the applications of an extended integral Ϝ-contraction and (ϰ,Ω-Ϝ)-contraction are given by providing an existence result in the solution of a fractional order multi-point boundary value problem involving the Riemann–Liouville fractional derivative. An interesting existence result for the solution of the nonlinear Fredholm integral equation of the second kind using the (ϰ,Γ1,2,Ω-Ϝ)-contraction has been proven. Herein, an example is established that explains how the Picard–Jungck sequence converges to the solution of the nonlinear integral equation. Examples are given for almost all the main results and some graphs are plotted where required.

Fixed-point theorems of {F}^{star}- ( psi,phi ) integral-type contractive conditions on 1_{E}-complete multiplicative partial cone metric spaces over Banach algebras and applications

In this paper, we introduce some user-friendly versions of integral-type fixed-point results and give some modifications of the classical Banach contraction principle by constructing a special type of contractive restrictions of integral forms for weak contraction mappings defined on 1_{E}-complete multiplicative partial cone metric spaces over Banach algebras and formulate some existence and uniqueness results regarding the fixed-point theorems using some integrative conditions. Moreover, we validate the significance our results and exploit them to find the unique solution of a fractional nonlinear differential equation of Caputo type, which complements some previously well-known generalizations found in the literature.

Contracting on average iterated function systems by metric change

We study contraction conditions for an iterated function system (IFS) of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space, which turn the IFS into one which is contracting on average. For the particular case of a system of C 1-diffeomorphisms of the circle which is proximal and does not have a probability measure simultaneously invariant by every map, we derive an equivalent metric which contracts on average and conclude that it carries a unique stationary probability measure. Here we strongly use local contraction properties established by Malicet in 2017, which then imply that the IFS has a negative random Lyapunov exponent and generalizes a result by Baxendale.

Fixed Point Results on Interval-Valued Fuzzy Metric Space using notation of Pairwise Compatible Maps and Occasionally Weakly Compatible Maps with Application

The purpose of the paper is to obtain common fixed point results on interval-valued fuzzy metric space for occasionally weakly compatible maps (OWC) using contractive conditions. With the concept of \(\tau\)norm, interval numbers, and some important properties of interval-valued \(\tau\)norm.

Existence of Common Coupled Fixed Points of Generalized Contractive Mappings in Ordered Multiplicative Metric Spaces

In order to generalize coupled fixed point results in the setup of partially ordered multiplicative metric spaces, we employing the concept of w∗- compatible mappings and generalized contractive condition and prove some coupled coincidence point and common coupled fixed points results. We also provide illustrative examples in support of our new results. Moreover, some applications to integral equations are presented. Our established results generalize, extend and unify various results in the existing literature.