Generalized Contraction Mappings Research Articles

Common Fixed Point Theorems on Generalized Ratio Contraction Mapping in Extended Rectangular b-Metric Spaces

In this paper, we propose and prove the common fixed point theorems on generalized contraction mappings in extended rectangular b-metric spaces by utilizing the weakly compatible function property.

Fixed Point Results for Generalized Contraction Mappings and Cyclical Mappings in b-Metric Spaces Endowed with a Digraph

Abstract In this paper, we establish a fixed point theorem for generalized contraction mappings in b-metric spaces endowed with a digraph. As an application of this result, we obtain fixed points of cyclical mappings in the setting of b-metric spaces. Our results extend and generalize several existing results in the literature.

Fixed Point Theorems of Generalized Contraction Mappings in Cone b-metric Spaces

Fixed Point Theorems of Generalized Contraction Mappings in Cone b-metric Spaces

Existence Results for a Class of Semilinear Fractional Partial Differential Equations with Delay in Banach Spaces

In this paper, we consider a class of nonlinear time fractional partial differential equations with delay. We obtain the existence and uniqueness of the mild solutions for the problem by the theory of solution operator and the general Banach contraction mapping principle. We need not extra conditions to ensure the contraction constant 0<k<1. Therefore, under some general conditions, we obtain our main results.

Solvability and construction of solution to the de la Vallee – Poussin problem for the second-order matrix Lyapunov equation with a parameter

The paper considers the issues of constructive analysis of the de la Vallee – Poussin boundary-value problem for the second-order linear matrix differential Lyapunov equation with a parameter and variable coefficients. The initial problem is reduced to an equivalent integral problem, and to study its solvability a modification of the generalized contraction mapping principle is used. A connection between the approach used and the Green’s function method is established. The coefficient sufficient conditions for the unique solvability of this problem are obtained. Using the Lyapunov – Poincaré small parameter method, an algorithm for constructing a solution has been developed. The convergence and the rate of convergence of this algorithm have been investigated, and a constructive estimation of the region of solution localization is given. To illustrate the application of the results obtained, the linear problem of steady heat conduction for a cylindrical wall, as well as a two-dimensional matrix model problem is considered. With the help of the developed general algorithm, analytical approximate solutions of these problems have been constructed and on the basis of their exact solutions a comparative numerical analysis has been carried out.

A Common Fixed Point Theorems for Generalized Contraction Mappings and Partially and Ordered Metric Spaces

The main aim of this paper, we prove some common fixed point results in the framework of metric and partially ordered metric spaces satisfying a generalized contractive condition of rational type. The proved results generalize and extend some known results in the literature.

Some common coupled fixed point theorems for generalized contraction mappings in C∗ algebras-valued b-metric spaces

In this paper, we establish the existence of common coupled fixed point and prove common coupled fixed point theorems for generalized contractive mappings in C∗ -algebras-valued b-metric spaces. Our results generalize some known results in C∗ -algebras-valued metric spaces.

Rational contraction in multiplicative metric spaces

The purpose of this paper is to prove that instead of a rational contraction shown in the papers Afrah A. N. Abdou, \emph{Fixed point theorems for generalized contraction mappings in multiplicative metric spaces, }J. Nonlinear Sci.Appl. 9, 2347-2363, (2016) and N. Sharma, K. Kumar, S. Sharma, R. Jha, \emph{Rational contractive conditionin multiplicative metric space and common fixed point theorem}, International Journal of Innovative Research in Science,Engineering and Technology, 5, 10473-10480 (2016) a more general contractive condition can be obtained in multiplicative metric spaces, which is equivalent to a contractive condition in metric spaces.

On new existence and uniqueness results concerning solutions to nonlinear Fredholm integral equations via w-distances and weak altering distance functions

The purpose of this work is to establish new fixed point theorems for generalized contraction mappings with respect to w-distances in complete metric spaces by using the concept of a weak altering distance function. Two illustrative examples are provided to advocate the usability of our results. Also, we present a numerical experiment for approximating a fixed point in these examples. As an application, the received results are used to summarize the existence and uniqueness of the solution for nonlinear Fredholm integral equations.

Fixed points of generalized contraction mappings in vector metric spaces

Fixed points of generalized contraction mappings in vector metric spaces

On new evolution of Ri\u2019s result via w-distances and the study on the solution for nonlinear integral equations and fractional differential equations

The aim of this work is to establish a new fixed point theorem for generalized contraction mappings with respect to w-distances in complete metric spaces. An illustrative example is provided to advocate the usability of our results. Also, we give a numerical experiment for approximating a fixed point in these examples. As an application, the received results are used to summarize the existence and uniqueness of the solution for nonlinear integral equations and nonlinear fractional differential equations of Caputo type.

Generalized contraction mappings of rational type and applications to nonlinear integral equations

The aim of the present paper is to introduce a new class of pair of contraction mappings, called ψ − (α, β, m)-contraction pairs, and obtain common fixed point theorems for a pair of mappings in this class, satisfying a minimal commutativity condition. Afterwards, we will use mappings in this class to analyze the existence of solutions for a class of nonlinear integral equations on the space of con- tinuous functions and in some of its subspaces. Concrete examples are also provided in order to illustrate the applicability of the results.

Optimal Linear Biased Estimation Based on Generalized Contraction Mapping

Estimation methods are generalized in this paper by the idea of “scalar-vector-matrix”. A generalized contraction mapping (GCM) framework is proposed for searching the optimal linear biased estimation. First, based on the latent model and the mean square error criterion, four different biased estimation methods are analyzed. They are the improved principal component estimation (PCE), the improved principal component estimation (IPCE), the ridge estimation (RE), and the generalized ridge estimation (GRE). A suboptimal ridge parameter for the RE is given. Four estimation performance theorems for the four methods are obtained using the traditional contraction mapping (CM) framework. The theoretical results can ease the difficulty of choosing methods for application. Second, we generalize the CM framework into the generalized contraction mapping (GCM) framework, and the optimal linear biased estimation method based GCM is given theoretically by the geometric tools of rotation, contraction, and reflection. Therefore, the GCM framework further improves the estimation performance. Finally, a numerical experiment is designed to validate the correctness of the theorems in the paper.

Fixed point theorems for generalized contraction mappings on b-rectangular metric spaces

In the present article, we study some fixed point theorems for a hybrid class of generalized contractive operators in the context of b-rectangular metric spaces. An open problem regarding to further generalizations for this type of operators is also given.

On Cyclic (α,β)-Admissible Generalized Contraction Mappings in Generalized Metric Spaces

On Cyclic (α,β)-Admissible Generalized Contraction Mappings in Generalized Metric Spaces

Fixed point theorems for a generalized contraction mapping of rational type in symmetric spaces

Abstract In this work, we establish some fixed point results for a contraction of rational type in symmetric spaces extending the fixed point theorems of Almeida, Roldan-Lopez-de-Hierro and Sadarangani [1].

Stability results for fixed point sets of α*- Ψ contractive multivalued mappings

In this paper, we established a stability result for fixed point sets associated with a sequence of multivalued mappings which belong to class of functions obtained by a multivalued extension of certain generalized contraction mapping. Certain other aspects of these mappings are already studied in the existing literatures. We also construct an illustrative example.

Generalized contraction mapping principle in locally convex topological vector spaces

Generalized contraction mapping principle in locally convex topological vector spaces

Fixed point theorems for generalized contraction mappings in multiplicative metric spaces

Fixed point theorems for generalized contraction mappings in multiplicative metric spaces

Caristi’s condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points

We consider a lower bounded function on a complete metric space. For this function, we obtain conditions, including Caristi’s conditions, under which this function attains its infimum. These results are applied to the study of the existence of a coincidence point of two mappings acting from one metric space to another. We consider both single-valued and set-valued mappings one of which is a covering mapping and the other is Lipschitz continuous. Special attention is paid to the study of a degenerate case that includes, in particular, generalized contraction mappings.