An inertial iterative method for solving split equality problem in Banach spaces

In this paper, a new self-adaptive algorithm with the inertial technique is proposed for solving the split equality problem in $ p $-uniformly convex and uniformly smooth Banach spaces. Under some mild control conditions, a strong convergence theorem for the proposed algorithm is established. Furthe...

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Published inAIMS mathematics Vol. 7; no. 10; pp. 17628 - 17646
Main Authors Wang, Meiying, Shi, Luoyi, Guo, Cuijuan
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
banach space
inertial technique
self-adaptive method
split equality problem
strong convergence
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ISSN2473-6988
2473-6988
DOI10.3934/math.2022971

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Abstract In this paper, a new self-adaptive algorithm with the inertial technique is proposed for solving the split equality problem in $ p $-uniformly convex and uniformly smooth Banach spaces. Under some mild control conditions, a strong convergence theorem for the proposed algorithm is established. Furthermore, the results are applied to split equality fixed point problem and split equality variational inclusion problem. Finally, numerical examples are provided to illustrate the convergence behaviour of the algorithm. The main results in this paper improve and generalize some existing results in the literature.
AbstractList In this paper, a new self-adaptive algorithm with the inertial technique is proposed for solving the split equality problem in p-uniformly convex and uniformly smooth Banach spaces. Under some mild control conditions, a strong convergence theorem for the proposed algorithm is established. Furthermore, the results are applied to split equality fixed point problem and split equality variational inclusion problem. Finally, numerical examples are provided to illustrate the convergence behaviour of the algorithm. The main results in this paper improve and generalize some existing results in the literature.
Author Shi, Luoyi
Wang, Meiying
Guo, Cuijuan
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SubjectTerms banach space
inertial technique
self-adaptive method
split equality problem
strong convergence
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Title An inertial iterative method for solving split equality problem in Banach spaces
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