A new self-adaptive method for solving resolvent of sum of two monotone operators in Banach spaces

We introduce a Tseng extragradient method for solving monotone inclusion problem in Banach space. A strong convergence result of an Halpern inertial extrapolation method for solving the resolvent of sum of two monotone operators without the knowledge of the Lipschitz constant was established. Lastly...

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Bibliographic Details
Published in:	Fixed point theory and algorithms for sciences and engineering Vol. 2023; no. 1; pp. 17 - 19
Main Authors:	Abass, H. A., Aphane, M., Oyewole, O. K.
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 11-12-2023 Springer Nature B.V SpringerOpen
Subjects:	Algorithms Analysis Applications of Mathematics Applied mathematics Banach spaces Bregman strongly nonexpansive mapping Differential Geometry Iterative method Iterative methods Knowledge Lipschitz continuous Mathematical and Computational Biology Mathematical programming Mathematics Mathematics and Statistics Methods Monotone inclusion problem Operators Topology Bregman strongly nonexpansive mapping 47H09 Monotone inclusion problem Iterative method 47J05 Lipschitz continuous 47J25 47H06
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Summary:	We introduce a Tseng extragradient method for solving monotone inclusion problem in Banach space. A strong convergence result of an Halpern inertial extrapolation method for solving the resolvent of sum of two monotone operators without the knowledge of the Lipschitz constant was established. Lastly, we illustrate some numerical behavior of our iterative scheme to showcase the performance of the proposed method compared to other related results in the literature.
ISSN:	2730-5422 2730-5422
DOI:	10.1186/s13663-023-00753-y