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Date Published: 23/09/2021
Online Published: 23/09/2021
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DOI: https://doi.org/10.54607/hcmue.js.18.9.3159(2021)
Issue
Vol. 18 No. 9 (2021): (English)
Section
Natural Sciences and Technology
How to Cite
Nguyễn , T. H. (2021). STRONG CONVERGENCE OF A HYBRID ITERATION FOR A GENERALIZED MIXED EQUILIBRIUM PROBLEM AND A BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES. HCMUE Journal of Science, 18(9), 1620. https://doi.org/10.54607/hcmue.js.18.9.3159(2021)

STRONG CONVERGENCE OF A HYBRID ITERATION FOR A GENERALIZED MIXED EQUILIBRIUM PROBLEM AND A BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES

Trung Hiếu Nguyễn

Main Article Content

Abstract

 

The purpose of this paper is to combine the Bregman distance with the shrinking projection method to introduce a new hybrid iteration process for a generalized mixed equilibrium problem and a Bregman totally quasi-asymptotically nonexpansive mapping. After that, under some suitable conditions, we prove that the proposed iteration strongly converges to the Bregman projection of the initial point onto the common element set of the solution set of a generalized mixed equilibrium problem and the fixed point set of a Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. This theorem extends and improves the results reported by Alizadeh and Moradlou (2016) from a generalized hybrid mapping and an equilibrium problem in Hilbert spaces to a Bregman totally quasi-asymptotically nonexpansive mapping and a generalized mixed equilibrium problem in reflexive Banach spaces. The result is applied to a generalized mixed equilibrium problem and a Bregman quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. In addition, an example is provided to illustrate the proposed iteration process.

 

Keywords

Bregman totally quasi-asymptotically nonexpansive mapping, generalized mixed equilibrium problem, hybrid iteration process, reflexive Banach spaces

Article Details

Author Biography

Trung Hiếu Nguyễn,

Nghiên cứu sinh chuyên ngành Toán Giải tích, Trường Đại học Sư phạm Thành phố Hồ Chí Minh

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