Taiwanese Journal of Mathematics

HALPERN TYPE ITERATIONS FOR STRONGLY QUASI-NONEXPANSIVE SEQUENCES AND ITS APPLICATIONS

Hadi Khatibzadeh and Sajad Ranjbar

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Abstract

In this paper, we study the strong convergence of the Halpern type algorithms for a strongly quasi-nonexpansive sequence of operators. These results extend the results of Saejung [11]. Some applications in infinite family of firmly quasi-nonexpansive mappings, multiparameter proximal point algorithm, constraint minimization and subgradient projection are presented.

Article information

Source
Taiwanese J. Math., Volume 19, Number 5 (2015), 1561-1576.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133724

Digital Object Identifier
doi:10.11650/tjm.19.2015.4700

Mathematical Reviews number (MathSciNet)
MR3412021

Zentralblatt MATH identifier
1357.47071

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H05: Monotone operators and generalizations 47J05: Equations involving nonlinear operators (general) [See also 47H10, 47J25]

Keywords
Halpern iteration fixed point strong convergence strongly quasi-nonexpansive sequence maximal monotone operator Halpern-Mann Proximal point algorithm

Citation

Khatibzadeh, Hadi; Ranjbar, Sajad. HALPERN TYPE ITERATIONS FOR STRONGLY QUASI-NONEXPANSIVE SEQUENCES AND ITS APPLICATIONS. Taiwanese J. Math. 19 (2015), no. 5, 1561--1576. doi:10.11650/tjm.19.2015.4700. https://projecteuclid.org/euclid.twjm/1499133724


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