Taiwanese Journal of Mathematics

ON AN OPEN QUESTION OF MOUDAFI FOR CONVEX FEASIBILITY PROBLEMS IN HILBERT SPACES

Eskandar Naraghirad

Full-text: Open access

Abstract

Very recently, Moudafi (Nonlinear Analysis 79 (2013) 117-121) introduced a relaxed alternating CQ-algorithm (RACQA) with weak convergence for the following convex feasibility problem: $$\mbox{Find}~x\in C,~y\in Q\hspace{0.4cm}\mbox{such that}~Ax=By, \tag{1.1}$$ where $H_1,~H_2,~H_3$ are real Hilbert spaces, $C\subset H_1$, $Q\subset H_2$ are two nonempty, closed and convex level sets, and $A:H_1\to H_3$, $B:H_2\to H_3$ are two bounded linear operators. In this paper, we will continue to consider the problem (1.1) and obtain a strongly convergent iterative sequence of Halpern-type to a solution of the problem and provide an affirmative answer to an open question posed by Moudafi in his recent work for convex feasibility problems in real Hilbert spaces. Furthermore, we study Halpern-type iterative schemes for finding common solutions of a convex feasibility problem and common fixed points of an infinite family of quasi-nonexpansive mappings in Hilbert spaces. Our results improve and generalize many known results in the current literature.

Article information

Source
Taiwanese J. Math., Volume 18, Number 2 (2014), 371-408.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706392

Digital Object Identifier
doi:10.11650/tjm.18.2014.3463

Mathematical Reviews number (MathSciNet)
MR3188509

Zentralblatt MATH identifier
1357.47074

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 37C25: Fixed points, periodic points, fixed-point index theory

Keywords
Halpern iterative scheme convex feasibility problem split common fixed-point problem quasi-nonexpansive mapping fixed point strong convergence

Citation

Naraghirad, Eskandar. ON AN OPEN QUESTION OF MOUDAFI FOR CONVEX FEASIBILITY PROBLEMS IN HILBERT SPACES. Taiwanese J. Math. 18 (2014), no. 2, 371--408. doi:10.11650/tjm.18.2014.3463. https://projecteuclid.org/euclid.twjm/1499706392


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