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

H. A. Abass; M. Aphane; O. K. Oyewole

doi:10.1186/s13663-023-00753-y

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

H. A. Abass^*, M. Aphane, O. K. Oyewole

^*Corresponding author for this work

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	17
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2023
Issue number	1
DOIs	https://doi.org/10.1186/s13663-023-00753-y
Publication status	Published - Dec 2023

Keywords

Bregman strongly nonexpansive mapping
Iterative method
Lipschitz continuous
Monotone inclusion problem

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10.1186/s13663-023-00753-y

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abstract = "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.",

keywords = "Bregman strongly nonexpansive mapping, Iterative method, Lipschitz continuous, Monotone inclusion problem",

author = "Abass, {H. A.} and M. Aphane and Oyewole, {O. K.}",

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AU - Oyewole, O. K.

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Y1 - 2023/12

N2 - 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.

AB - 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.

KW - Bregman strongly nonexpansive mapping

KW - Iterative method

KW - Lipschitz continuous

KW - Monotone inclusion problem

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ER -

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

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