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
Pages (from-to)	2823-2849
Number of pages	27
Journal	Optimization
Volume	72
Issue number	11
DOIs	https://doi.org/10.1080/02331934.2022.2076233
Publication status	Published - 2023
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",

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AU - Ali, B.

AU - Lawan, M. S.

AU - Ugwunnadi, G. C.

AU - Khan, A. R.

AU - Darvish, V.

PY - 2023

Y1 - 2023

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

UR - http://www.scopus.com/inward/record.url?scp=85130258825&partnerID=8YFLogxK

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DO - 10.1080/02331934.2022.2076233

M3 - Article

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SN - 0233-1934

VL - 72

SP - 2823

EP - 2849

JO - Optimization

JF - Optimization

IS - 11

ER -

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

Abstract

Keywords

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