A strong convergence theorem under a new shrinking projection method for nonlinear mappings in reflexive Banach spaces

B. Ali; M. S. Lawan; G. C. Ugwunnadi; A. R. Khan; V. Darvish

doi:10.1080/02331934.2022.2076233

A strong convergence theorem under a new shrinking projection method for nonlinear mappings in reflexive Banach spaces

B. Ali, M. S. Lawan, G. C. Ugwunnadi, A. R. Khan, V. Darvish^*

^*Corresponding author for this work

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

Abstract

In this paper, using a new shrinking projection method, we study the strong convergence theorem for finding a common point of the set of common fixed points of a finite family of Bregman demigeneralized mappings, common zero points of a finite family of Bregman inverse strongly monotone mappings and zero points of maximal monotone mapping in reflexive Banach space. Using this result, we get a new strong convergence theorem in Banach space. Our result extends and improves important recent results presented by many authors.

Original language	English
Journal	Optimization
DOIs	https://doi.org/10.1080/02331934.2022.2076233
Publication status	Accepted/In press - 2022
Externally published	Yes

Keywords

Bregman demigeneralized map
Bregman distance
fixed point
inverse strongly monotone map
maximal monotone map
shrinking projection method

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10.1080/02331934.2022.2076233

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title = "A strong convergence theorem under a new shrinking projection method for nonlinear mappings in reflexive Banach spaces",

abstract = "In this paper, using a new shrinking projection method, we study the strong convergence theorem for finding a common point of the set of common fixed points of a finite family of Bregman demigeneralized mappings, common zero points of a finite family of Bregman inverse strongly monotone mappings and zero points of maximal monotone mapping in reflexive Banach space. Using this result, we get a new strong convergence theorem in Banach space. Our result extends and improves important recent results presented by many authors.",

keywords = "Bregman demigeneralized map, Bregman distance, fixed point, inverse strongly monotone map, maximal monotone map, shrinking projection method",

author = "B. Ali and Lawan, {M. S.} and Ugwunnadi, {G. C.} and Khan, {A. R.} and V. Darvish",

note = "Funding Information: The authors wish to express their gratitude to the anonymous reviewers and the Associate editor for making very vital observations and comments that improve the presentation of the paper. The author A. R. Khan is grateful to King Fahd University of Petroleum and Minerals for supporting this research work. Publisher Copyright: {\textcopyright} 2022 Informa UK Limited, trading as Taylor & Francis Group.",

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doi = "10.1080/02331934.2022.2076233",

language = "English",

journal = "Optimization",

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AU - Ali, B.

AU - Lawan, M. S.

AU - Ugwunnadi, G. C.

AU - Khan, A. R.

AU - Darvish, V.

N1 - Funding Information: The authors wish to express their gratitude to the anonymous reviewers and the Associate editor for making very vital observations and comments that improve the presentation of the paper. The author A. R. Khan is grateful to King Fahd University of Petroleum and Minerals for supporting this research work. Publisher Copyright: © 2022 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2022

Y1 - 2022

N2 - In this paper, using a new shrinking projection method, we study the strong convergence theorem for finding a common point of the set of common fixed points of a finite family of Bregman demigeneralized mappings, common zero points of a finite family of Bregman inverse strongly monotone mappings and zero points of maximal monotone mapping in reflexive Banach space. Using this result, we get a new strong convergence theorem in Banach space. Our result extends and improves important recent results presented by many authors.

AB - In this paper, using a new shrinking projection method, we study the strong convergence theorem for finding a common point of the set of common fixed points of a finite family of Bregman demigeneralized mappings, common zero points of a finite family of Bregman inverse strongly monotone mappings and zero points of maximal monotone mapping in reflexive Banach space. Using this result, we get a new strong convergence theorem in Banach space. Our result extends and improves important recent results presented by many authors.

KW - Bregman demigeneralized map

KW - Bregman distance

KW - fixed point

KW - inverse strongly monotone map

KW - maximal monotone map

KW - shrinking projection method

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DO - 10.1080/02331934.2022.2076233

M3 - Article

AN - SCOPUS:85130258825

SN - 0233-1934

JO - Optimization

JF - Optimization

ER -

A strong convergence theorem under a new shrinking projection method for nonlinear mappings in reflexive Banach spaces

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Keywords

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