Accretive Operators In Banach Spaces Research Articles

Rates of Convergence and Metastability for Chidume’s Algorithm for the Approximation of Zeros of Accretive Operators in Banach Spaces

In this paper we give a quantitative analysis of an explicit iteration method due to C.E. Chidume for the approximation of a zero of an m-accretive operator A : X → 2 X in Banach spaces which does not involve the computation of the resolvent of A.

A novel algorithm with an inertial technique for fixed points of nonexpansive mappings and zeros of accretive operators in Banach spaces

<abstract><p>The purpose of this paper was to prove that a novel algorithm with an inertial approach, used to generate an iterative sequence, strongly converges to a fixed point of a nonexpansive mapping in a real uniformly convex Banach space with a uniformly Gâteaux differentiable norm. Furthermore, zeros of accretive mappings were obtained. The proposed algorithm has been implemented and tested via numerical simulation in MATLAB. The simulation results showed that the algorithm converges to the optimal configurations and shows the effectiveness of the proposed algorithm.</p></abstract>

The viscosity approximation method for accretive operators in Banach spaces

The viscosity approximation method for accretive operators in Banach spaces

A new iterative method based on the modified proximal-point algorithm for finding a common null point of an infinite family of accretive operators in Banach spaces

In this paper, we introduce and study a new iterative method for finding a common null point of an infinite family of accretive operators with a strongly accretive and Lipschitzian operator, by using the proximal-point algorithm. And also we prove that the common null point is a unique solution of variational inequality without imposing any compactness-type condition on either the operators or the space considered. Finally, some applications of the main results to equilibrium problems and fixed point problems with an infinite family of pseudocontractive mappings are given. The main result is a generalization and improvement of numerous well-known results in the available literature.

Newton–Kantorovich regularization method for nonlinear ill-posed equations involving $$m-$$accretive operators in Banach spaces

In this paper, we study nonlinear ill-posed problems involving $$m-$$accretive mappings in Banach spaces. We consider Newton–Kantorovich regularization method for the implementation of Lavrentiev regularization method. Using general Holder type source condition we obtain an error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060–2076, 2005) for choosing the regularization parameter.

Convergence Results for Fixed Point Problems of Accretive Operators in Banach Spaces

This paper deals with the approximate solutions of accretive maps in a uniformly convex Banach space. A weak convergence of a three - step iterative scheme involving the resolvents of accretive operators is proved. The main result is applied to a convex minimization problem in Hilbert spaces. In particular, the minimizer of a convex and proper lower semi-continuous function defined in a Hilbert space was obtained. Numerical illustration with graphical display of the convergence of the sequence obtained from the iterative scheme is also presented.

Zeros of accretive operators and asymptotics of a second order difference inclusion in Banach spaces

By developing new methods, we investigate the asymptotic behavior of solutions to a general second order difference inclusion of accretive type, and apply the results to approximate zeros of accretive operators in Banach spaces, and to optimization problems. Our results extend some previously known results in Hilbert and Banach spaces.

English

We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the lew available inertial-type methods for zeros of the sum of accretive operators in Banach spaces.

Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces

In this article, we study a modified viscosity splitting method combined with inertial extrapolation for accretive operators in Banach spaces and then establish a strong convergence theorem for such iterations under some suitable assumptions on the sequences of parameters. As an application, we extend our main results to solve the convex minimization problem. Moreover, the numerical experiments are presented to support the feasibility and efficiency of the proposed method.

Two new algorithms for finding a common zero of accretive operators in Banach spaces

Two new algorithms for finding a common zero of accretive operators in Banach spaces

Hybrid viscosity extragradient method for systems of variational inequalities, fixed points of nonexpansive mappings, zero points of accretive operators in Banach spaces

Hybrid viscosity extragradient method for systems of variational inequalities, fixed points of nonexpansive mappings, zero points of accretive operators in Banach spaces

On nonexpansive and accretive operators in Banach spaces

On nonexpansive and accretive operators in Banach spaces

Generalized viscosity implicit rules for solving quasi-inclusion problems of accretive operators in Banach spaces

The generalized viscosity implicit rules for solving quasi-inclusion problems of accretive operators in Banach spaces are established. The strong convergence theorems of the rules to a solution of quasi-inclusion problems of accretive operators are proved under certain assumptions imposed on the sequences of parameters. The results presented in this paper extend and improve the main results of Refs. (Moudafi, J Math Anal Appl. 2000;241:46–55; Xu et al., Fixed Point Theory Appl. 2015;2015:41; López et al., Abstr Appl Anal. 2012;2012; Cholamjiak, Numer Algor. DOI:10.1007/s11075-015-0030-6.). Moreover, some applications to monotone variational inequalities, convex minimization problem and convexly constrained linear inverse problem are presented.

Zero Point Problem of Accretive Operators in Banach Spaces

Splitting methods have recently received much attention due to the fact that many nonlinear problems arising in applied areas such as image recovery, signal processing and machine learning are mathematically modeled as a nonlinear operator equation and this operator is decomposed as the sum of two (possibly simpler) nonlinear operators. Most of the investigation on splitting methods is however carried out in the framework of Hilbert spaces. In this paper, we consider these methods in the setting of Banach spaces. We shall introduce a viscosity iterative forward–backward splitting method with errors to find zeros of the sum of two accretive operators in Banach spaces. We shall prove the strong convergence of the method under mild conditions. We also discuss applications of these methods to monotone variational inequalities, convex minimization problem and convexly constrained linear inverse problem.

Strong convergence result of forward–backward splitting methods for accretive operators in banach spaces with applications

Our interest in this paper is to prove strong convergence results for finding zeros of the sum of two accretive operators by utilizing a viscosity type forward–backward splitting method. We also discuss applications of this method to approximation of solution to certain integro-differential equation with generalized p-Laplacian operator. Our results complement many recent and important results in the literature.

Modified forward-backward splitting methods for accretive operators in Banach spaces

Modified forward-backward splitting methods for accretive operators in Banach spaces

Solution of a Variational inequality Problem for Accretive Operators in Banach Spaces

Solution of a Variational inequality Problem for Accretive Operators in Banach Spaces

Approximation common zero of two accretive operators in banach spaces

The purpose of this paper is to introduce a new iterative method that is the combination of the proximal point algorithm, viscosity approximation method and alternating resolvent method for finding the common zeros of two accretive operators in Banach spaces. And we will prove the strong convergence theorems for the iterative algorithms and give the example of the main theorems. The results of this paper are improvements and extensions of the corresponding ones announced by many others.

Domains of accretive operators in Banach spaces

LetD(A)be the domain of anm-accretive operatorAon a Banach spaceE. We provide sufficient conditions for the closure ofD(A)to be convex and forD(A)to coincide withEitself. Several related results and pertinent examples are also included.

Iterative Approximations for Zeros of Sum of Accretive Operators in Banach Spaces

We study the approximation of zero for sum of accretive operators using a modified Mann type forward-backward splitting algorithm and obtain strong convergence of the sequence generated by our scheme to the zero of sum of accretive operators in uniformly convex real Banach spaces which are also uniformly smooth. Our result is new and complements many recent and important results in this direction in the literature.