SOLVING MULTIPLE-SETS SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM IN REAL HILBERT SPACES.

Hammed Anuoluwapo Abass

doi:10.56082/annalsarscimath.2023.1-2.535

SOLVING MULTIPLE-SETS SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM IN REAL HILBERT SPACES.

Hammed Anuoluwapo Abass^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study and introduce a self adaptive method together with a Halpern iterative algorithm for approximating solutions of multiple-sets split monotone variational inclusion problem which includes the multiple-sets split feasibility problem, split feasibility problem, split monotone variational inclusion problem and split variational inclusion problem, to mention a few. Using our iterative algorithm, we prove a strong convergence result for approximating the solution of the aforementioned problems. Numerical examples on finite-dimensional and infinite-dimensional spaces are displayed to illustrate the performance of our iterative method. The result discussed in this article extends and complements many related results in literature.

Original language	English
Pages (from-to)	535-553
Number of pages	19
Journal	Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications
Volume	15
Issue number	1-2
DOIs	https://doi.org/10.56082/annalsarscimath.2023.1-2.535
Publication status	Published - 2023
Externally published	Yes

Keywords

Halpern method
Iterative method
Multiple-sets split monotone variational problem
fixed point problems

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10.56082/annalsarscimath.2023.1-2.535

Cite this

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title = "SOLVING MULTIPLE-SETS SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM IN REAL HILBERT SPACES.",

abstract = "In this paper, we study and introduce a self adaptive method together with a Halpern iterative algorithm for approximating solutions of multiple-sets split monotone variational inclusion problem which includes the multiple-sets split feasibility problem, split feasibility problem, split monotone variational inclusion problem and split variational inclusion problem, to mention a few. Using our iterative algorithm, we prove a strong convergence result for approximating the solution of the aforementioned problems. Numerical examples on finite-dimensional and infinite-dimensional spaces are displayed to illustrate the performance of our iterative method. The result discussed in this article extends and complements many related results in literature.",

keywords = "Halpern method, Iterative method, Multiple-sets split monotone variational problem, fixed point problems",

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AU - Abass, Hammed Anuoluwapo

PY - 2023

Y1 - 2023

N2 - In this paper, we study and introduce a self adaptive method together with a Halpern iterative algorithm for approximating solutions of multiple-sets split monotone variational inclusion problem which includes the multiple-sets split feasibility problem, split feasibility problem, split monotone variational inclusion problem and split variational inclusion problem, to mention a few. Using our iterative algorithm, we prove a strong convergence result for approximating the solution of the aforementioned problems. Numerical examples on finite-dimensional and infinite-dimensional spaces are displayed to illustrate the performance of our iterative method. The result discussed in this article extends and complements many related results in literature.

AB - In this paper, we study and introduce a self adaptive method together with a Halpern iterative algorithm for approximating solutions of multiple-sets split monotone variational inclusion problem which includes the multiple-sets split feasibility problem, split feasibility problem, split monotone variational inclusion problem and split variational inclusion problem, to mention a few. Using our iterative algorithm, we prove a strong convergence result for approximating the solution of the aforementioned problems. Numerical examples on finite-dimensional and infinite-dimensional spaces are displayed to illustrate the performance of our iterative method. The result discussed in this article extends and complements many related results in literature.

KW - Halpern method

KW - Iterative method

KW - Multiple-sets split monotone variational problem

KW - fixed point problems

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SN - 2066-5997

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EP - 553

JO - Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications

JF - Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications

IS - 1-2

ER -

SOLVING MULTIPLE-SETS SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM IN REAL HILBERT SPACES.

Abstract

Keywords

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