Viscosity approximation method for solving the multiple-set split equality common fixed-point problems for quasi-pseudocontractive mappings in Hilbert spaces

Adeolu Taiwo; Lateef Olakunle Jolaoso; Oluwatosin Temitope Mewomo

doi:10.3934/jimo.2020092

Article Contents

2021, Volume 17, Issue 5: 2733-2759. Doi: 10.3934/jimo.2020092

This issue Previous Article A proximal ADMM with the Broyden family for convex optimization problems Next Article The $ F $-objective function method for differentiable interval-valued vector optimization problems

Viscosity approximation method for solving the multiple-set split equality common fixed-point problems for quasi-pseudocontractive mappings in Hilbert spaces

School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

^* Corresponding author: Oluwatosin Temitope Mewomo
^* Corresponding author: Oluwatosin Temitope Mewomo

Received: April 30, 2019

Revised: January 31, 2020

Early access: May 2020

Published: September 2021

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Abstract

We propose a parallel iterative scheme with viscosity approximation method which converges strongly to a solution of the multiple-set split equality common fixed point problem for quasi-pseudocontractive mappings in real Hilbert spaces. We also give an application of our result to approximation of minimization problem from intensity-modulated radiation therapy. Finally, we present numerical examples to demonstrate the behaviour of our algorithm. This result improves and generalizes many existing results in literature in this direction.

Keywords:

Split equality common fixed point problem,
Lipschitzian quasi-pseudocontractive mapping,
viscosity approximation.

Mathematics Subject Classification: Primary: 47H10, 47J25; Secondary: 65J15.

Citation:

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Figure 1. Example 4.3. Top left: Case Ⅰ; Top right: Case Ⅱ; Bottom left: Case Ⅲ; Bottom right: Case Ⅳ

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Figure 2. Top left: Case IIa; Top right: Case IIb; Bottom left: Case IIc; Bottom right: Case IId

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Figure 3. Left : Case IIa* Right: Case IIc*

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Table 1. Numerical result for Example 4.3

		Algorithm 3.2	Algorithm 1.1
Case Ⅰ	No of Iter.	18	44
	CPU time (sec)	7.7529	9.7706
Case Ⅱ	No of Iter.	9	19
	CPU time (sec)	5.2116	8.8849
Case Ⅲ	No of Iter.	10	26
	CPU time (sec)	7.7204	12.7338
Case Ⅳ	No of Iter.	9	22
	CPU time (sec)	5.6424	7.1538

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Table 2. Numerical results

		Alg. (8)	Alg. Algorithm 3.2
Case IIa	CPU time (sec)	0.0019	8.8698e-4
	No of Iter.	75	16
Case IIb	CPU time (sec)	0.0020	8.6745e-4
	No. of Iter.	75	16
Case IIc	CPU time (sec)	0.0018	8.5652e-4
	No of Iter.	81	17
Case IId	CPU time (sec)	0.0019	8.9216e-4
	No of Iter.	74	16

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Table 3. Numerical results

		Alg. (8)	Alg. 3.2
Case IIa*	CPU time (sec)	0.0020	8.8533e-4
	No of Iter.	95	17
Case IIc*	CPU time (sec)	0.0021	8.6149e-4
	No of Iter.	103	18

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