Inertial Halpern-type iterative algorithm for the generalized multiple-set split feasibility problem in Banach spaces

In this paper, we study the generalized multiple-set split feasibility problem including the common fixed-point problem for a finite family of generalized demimetric mappings and the monotone inclusion problem in 2-uniformly convex and uniformly smooth Banach spaces. We propose an inertial Halpern-t...

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Published in:Journal of inequalities and applications 2024-01, Vol.2024 (1), p.7-24, Article 7
Main Author: Eslamian, Mohammad
Format: Article
Language:English
Subjects:
2-uniformly convex Banach space
Algorithms
Analysis
Applications of Mathematics
Applied mathematics
Banach spaces
Convergence
Feasibility
Generalized demimetric mappings
Hilbert space
Iterative algorithms
Mathematics
Mathematics and Statistics
Monotone inclusion problem
Multiple-set split feasibility problem
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description In this paper, we study the generalized multiple-set split feasibility problem including the common fixed-point problem for a finite family of generalized demimetric mappings and the monotone inclusion problem in 2-uniformly convex and uniformly smooth Banach spaces. We propose an inertial Halpern-type iterative algorithm for obtaining a solution of the problem and derive a strong convergence theorem for the algorithm. Then, we apply our convergence results to the convex minimization problem, the variational inequality problem, the multiple-set split feasibility problem and the split common null-point problem in Banach spaces.
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source Springer Nature - SpringerLink Journals - Fully Open Access ; ProQuest - Publicly Available Content Database
subjects 2-uniformly convex Banach space
Algorithms
Analysis
Applications of Mathematics
Applied mathematics
Banach spaces
Convergence
Feasibility
Generalized demimetric mappings
Hilbert space
Iterative algorithms
Mathematics
Mathematics and Statistics
Monotone inclusion problem
Multiple-set split feasibility problem
title Inertial Halpern-type iterative algorithm for the generalized multiple-set split feasibility problem in Banach spaces
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