Halpern-type iterative process for solving split common fixed point and monotone variational inclusion problem between Banach spaces

In this paper, we study the split common fixed point and monotone variational inclusion problem in uniformly convex and 2-uniformly smooth Banach spaces. We propose a Halpern-type algorithm with two self-adaptive stepsizes for obtaining solution of the problem and prove strong convergence theorem fo...

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Vydáno v:Numerical algorithms Ročník 86; číslo 4; s. 1359 - 1389
Hlavní autoři: Taiwo, A., Alakoya, T. O., Mewomo, O. T.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.04.2021
Springer Nature B.V
Témata:
Algebra
Algorithms
Banach spaces
Computer Science
Hilbert space
Inverse problems
Iterative methods
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Variational inclusion problem
47J22
Fixed point problem
47H10
Relatively nonexpansive mapping
Halpern iteration
Self-adaptive method
Banach spaces
47J25
65J15
ISSN:1017-1398, 1572-9265
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Shrnutí:In this paper, we study the split common fixed point and monotone variational inclusion problem in uniformly convex and 2-uniformly smooth Banach spaces. We propose a Halpern-type algorithm with two self-adaptive stepsizes for obtaining solution of the problem and prove strong convergence theorem for the algorithm. Many existing results in literature are derived as corollary to our main result. In addition, we apply our main result to split common minimization problem and fixed point problem and illustrate the efficiency and performance of our algorithm with a numerical example. The main result in this paper extends and generalizes many recent related results in the literature in this direction.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-00937-2