Split equality fixed point problems of quasi-nonexpansive operators in Hilbert spaces

Dianlu Tian; Lining Jiang; Luoyi Shi; Rudong Chen

doi:10.23952/jnfa.2019.11

Split equality fixed point problems of quasi-nonexpansive operators in Hilbert spaces

Dianlu Tian^*
, Lining Jiang
, Luoyi Shi
, Rudong Chen

^*Corresponding author for this work

School of Mathematics and Statistics

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

1 Citation (Scopus)

Abstract

Let H₁,H₂,H₃ be three Hilbert spaces. Let T₁ : H₁ → H₁ and T₂ : H₂ → H₂ be two quasi-nonexpansive operators. Let A : H₁ → H₃ and B : H₂ → H₃ be two bounded and linear operators. The split equality fixed point problem of quasi-nonexpansive operators is to find x ∈ H₁ and y ∈ H₂ such that x = T₁x, y = T₂y and Ax = By. In this paper, we introduce an iterative algorithm to solve the split equality fixed point problem. We show that the proposed algorithm is strongly convergent without any compactness imposed on the operators.

Original language	English
Article number	11
Journal	Journal of Nonlinear Functional Analysis
Volume	2019
DOIs	https://doi.org/10.23952/jnfa.2019.11
Publication status	Published - 2019

Keywords

Split common fixed point problem
Split equality problem
Split feasibility problem

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10.23952/jnfa.2019.11

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abstract = "Let H1,H2,H3 be three Hilbert spaces. Let T1 : H1 → H1 and T2 : H2 → H2 be two quasi-nonexpansive operators. Let A : H1 → H3 and B : H2 → H3 be two bounded and linear operators. The split equality fixed point problem of quasi-nonexpansive operators is to find x ∈ H1 and y ∈ H2 such that x = T1x, y = T2y and Ax = By. In this paper, we introduce an iterative algorithm to solve the split equality fixed point problem. We show that the proposed algorithm is strongly convergent without any compactness imposed on the operators.",

keywords = "Split common fixed point problem, Split equality problem, Split feasibility problem",

author = "Dianlu Tian and Lining Jiang and Luoyi Shi and Rudong Chen",

note = "Publisher Copyright: {\textcopyright} 2019 Journal of Nonlinear Functional Analysis.",

year = "2019",

doi = "10.23952/jnfa.2019.11",

language = "English",

volume = "2019",

journal = "Journal of Nonlinear Functional Analysis",

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TY - JOUR

T1 - Split equality fixed point problems of quasi-nonexpansive operators in Hilbert spaces

AU - Tian, Dianlu

AU - Jiang, Lining

AU - Shi, Luoyi

AU - Chen, Rudong

PY - 2019

Y1 - 2019

N2 - Let H1,H2,H3 be three Hilbert spaces. Let T1 : H1 → H1 and T2 : H2 → H2 be two quasi-nonexpansive operators. Let A : H1 → H3 and B : H2 → H3 be two bounded and linear operators. The split equality fixed point problem of quasi-nonexpansive operators is to find x ∈ H1 and y ∈ H2 such that x = T1x, y = T2y and Ax = By. In this paper, we introduce an iterative algorithm to solve the split equality fixed point problem. We show that the proposed algorithm is strongly convergent without any compactness imposed on the operators.

AB - Let H1,H2,H3 be three Hilbert spaces. Let T1 : H1 → H1 and T2 : H2 → H2 be two quasi-nonexpansive operators. Let A : H1 → H3 and B : H2 → H3 be two bounded and linear operators. The split equality fixed point problem of quasi-nonexpansive operators is to find x ∈ H1 and y ∈ H2 such that x = T1x, y = T2y and Ax = By. In this paper, we introduce an iterative algorithm to solve the split equality fixed point problem. We show that the proposed algorithm is strongly convergent without any compactness imposed on the operators.

KW - Split common fixed point problem

KW - Split equality problem

KW - Split feasibility problem

UR - https://www.scopus.com/pages/publications/85067389842

U2 - 10.23952/jnfa.2019.11

DO - 10.23952/jnfa.2019.11

M3 - Article

AN - SCOPUS:85067389842

SN - 2052-532X

VL - 2019

JO - Journal of Nonlinear Functional Analysis

JF - Journal of Nonlinear Functional Analysis

M1 - 11

ER -

Split equality fixed point problems of quasi-nonexpansive operators in Hilbert spaces

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