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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Vydáno v:Optimization Ročník 74; číslo 2; s. 343 - 364
Hlavní autoři: Xu, H.-Y., Lan, H.-Y., Zhao, Y., Ye, Y.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Taylor & Francis 25.01.2025
Taylor & Francis LLC
Témata:
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
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2023.2256968