Inertial Mann-Type iterative method for solving split monotone variational inclusion problem with applications

Jacob Ashiwere Abuchu; Godwin Chidi Ugwunnadi; Ojen Kumar Narain

doi:10.3934/jimo.2022075

Article Contents

2023, Volume 19, Issue 4: 3020-3043. Doi: 10.3934/jimo.2022075

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Inertial Mann-Type iterative method for solving split monotone variational inclusion problem with applications

1.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
2.
Department of Mathematics University of Calabar, Calabar Nigeria
3.
Department of Mathematics University of Eswatini, Private Bag 4 Kwaluseni Eswatini
4.
Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University, Pretoria South Africa

^*Corresponding author: Jacob Ashiwere Abuchu
^*Corresponding author: Jacob Ashiwere Abuchu

Received: January 2022

Revised: March 2022

Published: April 2023

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Abstract

In this paper, we study a modified relaxed inertial Mann-type iterative algorithm for solving split monotone variational inclusion problem without prior knowledge of the bounded linear operator norm in real Hilbert spaces. Under some appropriate assumptions on the parameters, we established a strong convergence result of the proposed algorithm. As applications, some special cases of the general problem are given. Finally, we also give some numerical illustrations of the proposed method in comparison with other methods in the literature to show the applicability and advantage of our results.

Keywords:

Split monotone variational inclusion problem,
inertial iterative method,
strong convergence,
nonexpansive operator,
average operator,
inverse strongly monotone.

Mathematics Subject Classification: Primary: 47H09; Secondary: 47J25.

Citation:

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Figure 1. Plot of Errors against Iterations number (n): Case Ⅰ

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Figure 2. Plot of Errors against Iterations number (n): Case Ⅱ

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Figure 3. Plot of Errors against Iterations number (n): Case Ⅲ

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Figure 4. Plot of Errors against Iterations number (n): Case Ⅳ

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Table 1. Numerical Result for Example 5.1

Cases		Algorithm (1.10)	Algorithm 3.2
Case Ⅰ	Sec.	32.2782	21.8243
	No of Iter.	24	9
Case Ⅱ	Sec.	35.5980	11.1867
	No of Iter.	24	9
Case Ⅲ	Sec.	67.1801	36.5033
	No of Iter.	27	10
Case Ⅳ	Sec.	58.9075	27.9240
	No of Iter.	30	10

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