Generalized Contraction Mappings Research Articles

A novel iterative process for numerical reckoning of fixed points via generalized nonlinear mappings with qualitative study

Abstract This manuscript is devoted to constructing a novel iterative scheme and reckoning of fixed points for generalized contraction mappings in hyperbolic spaces. Also, we establish Δ \Delta and strong convergence results by the considered iteration under the class of mappings satisfying condition (E). Moreover, some qualitative results of the suggested iteration, like weak w 2 {w}^{2} -stability and data dependence results, are discussed. Furthermore, to test the efficiency and effectiveness of the proposed iteration, practical experiments are given. To support the theoretical results, illustrative examples are presented. Finally, our results improve and generalize several classical results in the literature of fixed point iterations.

Some common fixed point theorems using G-Cone metric spaces with Banach algebra

In this paper, we have proved some common fixed point results using generalized contraction mapping in G-cone metric spaces over Banach algebras. Our results are a generalization and extension of several well-known results related to fixed point theory.

Some Results Regarding \(\varphi\) -maps on G-Cone Metric Spaces with Banach Algebra

Aims/ objectives: In our study, we used generalized contraction mapping in G-cone metric space with Banach algebras to establish various fixed point and common fixed point results. Beg [1] defines this space in terms of a few contractive conditions on \(\varphi\) -maps. Our outcomes are a generalization and an extension of several well-known fixed point results.

Rational Contraction in Metric Space and Common Fixed Point Theorems

The study of contraction mappings in fixed-point theory is a fascinating and crucial field of mathematics. The concept of contraction plays a vital role in proving the existence and uniqueness of fixed points. Banach's contraction theory offers a fixed point theorem that is widely accepted as unique in most analyses. By using rational expressions in metric spaces, we can achieve unique results in general contraction mapping. These results are based on several innovative ideas stemming from the latest research. The delivered results upgrade and federate many existing outcomes on the topic in the literature Bhardwaj, R. et al. (2007) Chouhan et al. (2014) and Garg and Priyanka (2016). Also gives some suitable examples for verifying our results.

Convex (α, β)-Generalized Contraction and Its Applications in Matrix Equations

This paper investigates the existence and convergence of solutions for linear and nonlinear matrix equations. This study explores the potential of convex (α,β)-generalized contraction mappings in geodesic spaces, ensuring the existence of solutions for both linear and nonlinear matrix equations. This paper extends the concept to partially ordered geodesic spaces and establishes new existence and convergence results. Illustrative examples are provided to demonstrate the practical relevance of the findings. Overall, this research contributes a novel approach to the field of matrix equations.

Some Fixed Point Results for α-Admissible mappings on Quasi Metric Space Via θ-Contractions

By employing α-admissible mapping, this study expands and investigates generalized contraction mappings in quasi-metric spaces, aiming to establish the existence of fixed points. Moreover, we show that the main outcomes of the paper encompass several previously reported results in the literature.

Existence of a system of fractional order differential equations via generalized contraction mapping in partially ordered Banach space

Existence of a system of fractional order differential equations via generalized contraction mapping in partially ordered Banach space

Generalized contraction mappings in double controlled metric type space and related fixed point theorems

In this article, we introduce two new types of generalized contraction mappings in double controlled metric type spaces: Θ-double controlled contraction mapping and Ćirić-Reich-Rus-type-Θ-double controlled contraction mapping. For each contraction mapping, we establish the existence and uniqueness of the fixed point theorems on the complete double controlled metric type space and provide examples. We present an application of our results and demonstrate how our results generalize several existing fixed point theorems in the literature.

Learning Reliable Neural Networks with Distributed Architecture Representations

Neural architecture search (NAS) has shown the strong performance of learning neural models automatically in recent years. But most NAS systems are unreliable due to the architecture gap brought by discrete representations of atomic architectures. In this article, we improve the performance and robustness of NAS via narrowing the gap between architecture representations. More specifically, we apply a general contraction mapping to model neural networks with distributed representations (Neural Architecture Search with Distributed Architecture Representations (ArchDAR)). Moreover, for a better search result, we present a joint learning approach to integrating distributed representations with advanced architecture search methods. We implement our ArchDAR in a differentiable architecture search model and test learned architectures on the language modeling task. On the Penn Treebank data, it outperforms a strong baseline significantly by 1.8 perplexity scores. Also, the search process with distributed representations is more stable, which yields a faster structural convergence when it works with the differentiable architecture search model.

A relation theoretic <i>m</i>-metric fixed point algorithm and related applications

<abstract><p>In this article, we introduce the concept of generalized rational type $ F $ -contractions on relation theoretic <italic>m</italic>-metric spaces (denoted as $ F_{R}^{m} $-contractions, where $ R $ is a binary relation) and some related fixed point theorems are provided. Then, we achieve some fixed point results for cyclic rational type $ F_{R}^{m} $- generalized contraction mappings. Moreover, we state some illustrative numerically examples to show our results are true and meaningful. As an application, we discuss a positive definite solution of a nonlinear matrix equation of the form $ \Lambda = S+\sum\limits_{i = 1}^{\mu }Q_{i}^{\ast }\Xi \left(\Lambda \right) Q_{i} $.</p></abstract>

On fixed-point approximations for a class of nonlinear mappings based on the JK iterative scheme with application

<abstract><p>The goal of this manuscript is to introduce the JK iterative scheme for the numerical reckoning of fixed points in generalized contraction mappings. Also, weak and strong convergence results are investigated under this scheme in the setting of Banach spaces. Moreover, two numerical examples are given to illustrate that the JK iterative scheme is more effective than some other iterative schemes in the literature. Ultimately, as an application, the JK iterative scheme is applied to solve a discrete composite functional differential equation of the Volterra-Stieljes type.</p></abstract>

A tripled coincidence point technique for solving integral equations via an upper class of type II

<abstract><p>The goal of this paper is to obtain some tripled coincidence point results for generalized contraction mappings in the setting of $ JS $-metric spaces endowed with a partial order. Furthermore, illustrative examples to support the theoretical results and the application are obtained. Finally, some theoretical results are applied to discuss the existence of a solution for a system of non-homogeneous and homogeneous integral equations as applications.</p></abstract>

Generalization of Fixed Point Approximation of Contraction and Suzuki Generalized Non-Expansive Mappings in Banach Domain

By principal motivation from the results of the new iterative scheme that produces faster results than K-iteration. In this article, we study generalized results by a new iteration scheme to approximate fixed points of generalized contraction and Suzuki non-expansive mappings. We establish strong convergence results of generalized contraction mappings of closed convex Banach space and also deduce data dependent results. Furthermore, we prove some weak and strong convergence theorems in the sense of generalized Suzuki non-expansive mapping by applying condition (C).

A generalized contraction mapping applied in solving modified implicit $$\phi $$-Hilfer pantograph fractional differential equations

A generalized contraction mapping applied in solving modified implicit $$\phi $$-Hilfer pantograph fractional differential equations

Fixed point theorems of generalized contraction mappings on ϖ-cone metric spaces over banach algebras

Without the assumptions of normality and solidness, we investigate some properties of cones with some semiinterior points in normed algebras, introduce two novel notions of S-set and S-number associated with every semiinterior point in the underlying cone, give a constructive example with calculations of these new quantities, study some topological characterization of the topology induced by ϖ-cone metric of ϖ-cone metric space over Banach algebra with the help of semiinterior points instead of interior points, and then generalize some fixed point theorems of contraction type mapping defined on ϖ-cone metric space over Banach algebra with nonnormal and nonsolid cone.

A Fixed Point Approach to the Hyers-Ulam-Rassias Stability Problem of Pexiderized Functional Equation in Modular Spaces

Abstract In this paper, we consider pexiderized functional equations for studying their Hyers-Ulam-Rassias stability. This stability has been studied for a variety of mathematical structures. Our framework of discussion is a modular space. We adopt a fixed-point approach to the problem in which we use a generalized contraction mapping principle in modular spaces. The result is illustrated with an example.

On inertial type algorithms with generalized contraction mapping for solving monotone variational inclusion problems

On inertial type algorithms with generalized contraction mapping for solving monotone variational inclusion problems

On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses

In this paper, we consider the initial boundary value problem for a class of nonlinear fractional partial integro-differential equations of mixed type with non-instantaneous impulses in Banach spaces. Sufficient conditions of existence and uniqueness of PC-mild solutions for the equations are obtained via general Banach contraction mapping principle, Krasnoselskii’s fixed point theorem, and α-order solution operator.

Fixed Point Theorem for Cyclic Weakly Generalized Contraction Mapping of Ciric Type

In this article, the concept of cyclic weakly generalized contraction mapping of Ciric type has been introduced and the existence of a fixed point for such mappings in the setup of complete metric spaces has been established. Result obtained extends and improves some fixed point results in the literature. Example is also given to show that class of contraction mappings introduced in the paper is strictly larger class than the class of mappings used in the literature and thus ensures wider applicability of the result by producing the solutions to new problems.

Existence and Uniqueness of Mild Solutions for Fractional Partial Integro-Differential Equations

In this paper, we study a class of nonlinear time fractional partial integro-differential equations. The main results for the problem are obtained by the measure of noncompactness, solution operator, convex-power condensing operator and general Banach contraction mapping principle.