Split Common Null Point Problem Research Articles

Two Modified Inertial Algorithms for a Class of Split Common Null Point Problems with Demi-Contractive Mapping

Two Modified Inertial Algorithms for a Class of Split Common Null Point Problems with Demi-Contractive Mapping

Split common null point problem for generalized monotone operators

ABSTRACT In this article, we present some properties of the resolvent of maximally comonotone (generalized monotone) operators in Hilbert spaces. Also, we study the split common null point problem for a finite family of maximally comonotone operators in Hilbert spaces. For solving this split common null point problem, we propose an inertial algorithm with the step size independent on the prior estimate of the norm of the bounded linear operators and prove strong convergence theorem for this inertial algorithm. The obtained result of this article complements many recent results in this direction.

Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem

In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems (SpCNPP) in such a way that the Halpern iteration and inertial extrapolation are computed simultaneously in the beginning of each iteration. We prove the strong convergence of sequences driven by the suggested methods without estimating the norm of bounded linear operator when certain appropriate assumptions are made. We demonstrate the efficiency of our iterative methods and compare them with some related and well-known results using relevant numerical examples.

Inertial Halpern-type iterative algorithm for the generalized multiple-set split feasibility problem in Banach spaces

In this paper, we study the generalized multiple-set split feasibility problem including the common fixed-point problem for a finite family of generalized demimetric mappings and the monotone inclusion problem in 2-uniformly convex and uniformly smooth Banach spaces. We propose an inertial Halpern-type iterative algorithm for obtaining a solution of the problem and derive a strong convergence theorem for the algorithm. Then, we apply our convergence results to the convex minimization problem, the variational inequality problem, the multiple-set split feasibility problem and the split common null-point problem in Banach spaces.

The AA-Viscosity Algorithm for Fixed-Point, Generalized Equilibrium and Variational Inclusion Problems

The aim of this paper is to propose an inertial-type AA-viscosity algorithm for approximating the common solutions of the split variational inclusion problem, the generalized equilibrium problem and the common fixed-point problem of nonexpansive mappings. The strong convergence of an iterative sequence obtained through the proposed method is proved under some mild assumptions. Consequently, approximations of the solution of the split feasibility problem, the relaxed split feasibility problem, the split common null point problem and the split minimization problem are given. The applicability of our proposed algorithm has been illustrated with the help of a numerical example. Our iterative method was then compared graphically with different comparable methods in the existing literature.

New inertial self-adaptive algorithms for the split common null-point problem: application to data classifications

In this paper, we propose two inertial algorithms with a new self-adaptive step size for approximating a solution of the split common null-point problem in the framework of Banach spaces. The step sizes are adaptively updated over each iteration by a simple process without the prior knowledge of the operator norm of the bounded linear operator. Under suitable conditions, we prove the weak-convergence results for the proposed algorithms in p-uniformly convex and uniformly smooth Banach spaces. Finally, we give several numerical results in both finite- and infinite-dimensional spaces to illustrate the efficiency and advantage of the proposed methods over some existing methods. Also, data classifications of heart diseases and diabetes mellitus are presented as the applications of our methods.

A Modified Viscosity-Type Self-Adaptive Iterative Algorithm for Common Solution of Split Problems with Multiple Output Sets in Hilbert Spaces

A modified viscosity-type self-adaptive iterative algorithm is presented in this study, having a strong convergence theorem for estimating the common solution to the split generalized equilibrium problem along with the split common null point problem with multiple output sets, subject to some reasonable control sequence restrictions. The suggested algorithm and its immediate consequences are also discussed. The effectiveness of the proposed algorithm is finally demonstrated through analytical examples. The findings presented in this paper will help to consolidate, extend, and improve upon a number of recent findings in the literature.

A unified scheme for solving split inclusions with applications

In this article, we propose an iterative scheme for solving a generalized split common null point problem. The iterative method uses self‐adaptive stepsizes that do not depend on the Lipschitz constants of the underlying operators. Instead, the stepsizes are updated using a simple updating formula. We prove the strong convergence theorems of the sequence generated by the iterative scheme under some mild assumptions. Furthermore, we derive iterative methods for solving split generalized variational inequality, convex feasibility, and minimization problems. In addition, some numerical illustrations are provided to support the main result.

Two-step inertial method for solving split common null point problem with multiple output sets in Hilbert spaces

<abstract><p>In this paper, an algorithm with two-step inertial extrapolation and self-adaptive step sizes is proposed to solve the split common null point problem with multiple output sets in Hilbert spaces. Weak convergence analysis are obtained under some easy to verify conditions on the iterative parameters in Hilbert spaces. Preliminary numerical tests are performed to support the theoretical analysis of our proposed algorithm.</p></abstract>

An inertially constructed projection based hybrid algorithm for fixed point and split null point problems

<abstract><p>In this paper, we posit a framework for the investigation of the fixed point problems (FPP) involving an infinite family of $ \Bbbk $-demicontractive operators and the split common null point problems (SCNPP) in Hilbert spaces. We employ an accelerated variant of the hybrid shrinking projection algorithm for the construction of a common solution associated with the FPP and SCNPP. Theoretical results comprise strong convergence characteristics under suitable sets of constraints as well as numerical results are established for the underlying algorithm. Applications to signal processing as well as various abstract problems are also incorporated.</p></abstract>

A Novel Algorithm for Generalized Split Common Null Point Problem with Applications

A Novel Algorithm for Generalized Split Common Null Point Problem with Applications

Convergence analysis of the shrinking approximants for fixed point problem and generalized split common null point problem

In this paper, we compute a common solution of the fixed point problem (FPP) and the generalized split common null point problem (GSCNPP) via the inertial hybrid shrinking approximants in Hilbert spaces. We show that the approximants can be easily adapted to various extensively analyzed theoretical problems in this framework. Finally, we furnish a numerical experiment to analyze the viability of the approximants in comparison with the results presented in (Reich and Tuyen in Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 114:180, 2020).

A self-adaptive method for split common null point problems and fixed point problems for multivalued Bregman quasi-nonexpansive mappings in Banach spaces

In this paper, we propose a self-adaptive algorithm for solving the split common null point problem and the fixed point problem for multivalued Bregman quasi-nonexpansive mappings in Banach spaces. We prove that the sequence generated by our iterative scheme converges strongly to a common solution of the above-mentioned problems under some suitable conditions. We also apply our main result to split feasibility problems in Banach spaces. Finally, numerical examples are given to support our main theorem. The results presented in this paper improve and extend many recent results in the literature.

A split common fixed point and null point problem for Lipschitzian $J-$quasi pseudocontractive mappings in Banach spaces

A split common fixed point and null point problem (SCFPNPP) which includes the split common fixed point problem, the split common null point problem and other problems related to the fixed point problem and the null point problem is studied. We introduce a Halpern--Ishikawa type algorithm for studying the split common fixed point and null point problem for Lipschitzian $J-$quasi pseudocontractive operators and maximal monotone operators in real Banach spaces. Moreover, we establish a strong convergence results under some suitable conditions and reduce our main result to the above-mentioned problems. Finally, we applied the study to split feasibility problem (FEP), split equilibrium problem (SEP), split variational inequality problem (SVIP) and split optimization problem (SOP).

New Self-Adaptive Inertial-like Proximal Point Methods for the Split Common Null Point Problem

Symmetry plays an important role in solving practical problems of applied science, especially in algorithm innovation. In this paper, we propose what we call the self-adaptive inertial-like proximal point algorithms for solving the split common null point problem, which use a new inertial structure to avoid the traditional convergence condition in general inertial methods and avoid computing the norm of the difference between xn and xn−1 before choosing the inertial parameter. In addition, the selection of the step-sizes in the inertial-like proximal point algorithms does not need prior knowledge of operator norms. Numerical experiments are presented to illustrate the performance of the algorithms. The proposed algorithms provide enlightenment for the further development of applied science in order to dig deep into symmetry under the background of technological innovation.

An iterative algorithm with inertial technique for solving the split common null point problem in Banach spaces

In this work, we introduce a modified inertial algorithm for solving the split common null point problem without the prior knowledge of the operator norms in Banach spaces. The strong convergence theorem of our method is proved under suitable assumptions. We apply our result to the split feasibility problem, split equilibrium problem and split minimization problem. Finally, we provide some numerical experiments including compressed sensing to illustrate the performances of the proposed method. The result presented in this paper improves and generalizes many recent important results in the literature.

An inertial self-adaptive algorithm for the generalized split common null point problem in Hilbert spaces

An inertial self-adaptive algorithm for the generalized split common null point problem in Hilbert spaces

Strong convergence theorem for common zero points of inverse strongly monotone mappings and common fixed points of generalized demimetric mappings

In this paper, we introduce a new and efficient algorithm for finding a common element of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common zero points of a finite family of inverse strongly monotone mappings in Hilbert spaces. Strong convergence of the proposed algorithm is established under standard and mild conditions in a Hilbert space. As an application, we use our algorithm for solving the common solutions to the variational inequality problem, the common minimization problem, the multiple-set split feasibility problem, the split common fixed point problem and the split common null point problem.

Convergence analysis of new inertial method for the split common null point problem

ABSTRACT In this paper, we propose a new iterative method with alternated inertial step for solving split common null point problem in real Hilbert spaces. We obtain weak convergence of the proposed iterative algorithm. Furthermore, we introduce the notion of bounded linear regularity property for the split common null point problem and obtain the linear convergence property for the new algorithm under some mild assumptions. Finally, we provide some numerical examples to demonstrate the performance and efficiency of the proposed method.

Inertial algorithm with self-adaptive step size for split common null point and common fixed point problems for multivalued mappings in Banach spaces

ABSTRACT In this article we introduce an inertial iterative scheme with self-adaptive step size for finding a common solution of split common null point problem for a finite family of maximal monotone operators and fixed point problem for a finite family of multivalued demicontractive mappings between a Banach space and Hilbert space. Strong convergence result is obtained for the proposed algorithm. The self-adaptive step size ensures no requirement for a prior knowledge or estimate of the norm of the operator. The inertial term introduced in the algorithm is efficient, it helps to avoid imposing some strong conditions usually used for inertial-type algorithms by many authors. We give some applications of our results to game theory, split equilibrium and minimum-norm problems. Numerical experiment is also presented to demonstrate the efficiency of our proposed method as well as comparing with other existing method in the literature. Our results improve and generalize many well known results in this direction in the literature.