Novel extended Halpern-type convergence algorithms for the split common fixed point problem involving α-demicontractive operators

As is well known, it is quite valuable and challenging to solve the split common fixed point problem (SCFP) associated with two different nonlinear operators. In this study, in order to solve (SCFP) with a more general setting of α-demicontractive operators due to Măruşter and Măruşter in 2011, we d...

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Bibliographic Details
Published in:Optimization Vol. 74; no. 2; pp. 343 - 364
Main Authors: Xu, H.-Y., Lan, H.-Y., Zhao, Y., Ye, Y.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 25.01.2025
Taylor & Francis LLC
Subjects:
Algorithms
Convergence
Fixed points (mathematics)
Hilbert space
infinite dimensional Hilbert space
novel extended Halpern-type iterative algorithm
Operators
split common fixed point problem
Strong convergence
α-demicontractive operator
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:As is well known, it is quite valuable and challenging to solve the split common fixed point problem (SCFP) associated with two different nonlinear operators. In this study, in order to solve (SCFP) with a more general setting of α-demicontractive operators due to Măruşter and Măruşter in 2011, we develop a kind of novel iterative approach in infinite dimensional Hilbert spaces. Further, using Xu's inequality and Maingé's lemma, strong convergence theorems of the suggested algorithms are established under some mild conditions. Finally, some special cases are considered, and the main results of this work are supported via two numerical comparisons.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2023.2256968