Taiwanese Journal of Mathematics

IMPLICIT AND EXPLICIT ALGORITHMS FOR MINIMUM-NORM FIXED POINTS OF PSEUDOCONTRACTIONS IN HILBERT SPACES

Yonghong Yao, Vittorio Colao, Giuseppe Marino, and Hong-Kun Xu

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Abstract

We introduce implicit and explicit iterative algorithms for the construction of fixed points of pseudocontractions $T$ in Hilbert spaces. We prove that the proposed iterative algorithms converge strongly to the minimum-norm fixed point of $T$. Moreover we show that some of the existing iterative algorithms for nonexpansive mappings fail to converge when applied to pseudocontractions.

Article information

Source
Taiwanese J. Math., Volume 16, Number 4 (2012), 1489-1506.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406745

Digital Object Identifier
doi:10.11650/twjm/1500406745

Mathematical Reviews number (MathSciNet)
MR2951149

Zentralblatt MATH identifier
1293.47068

Subjects
Primary: 47H05: Monotone operators and generalizations 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H17

Keywords
iterative algorithm implicit explicit minimum-norm fixed point pseudocontraction nonexpansive mapping projection

Citation

Yao, Yonghong; Colao, Vittorio; Marino, Giuseppe; Xu, Hong-Kun. IMPLICIT AND EXPLICIT ALGORITHMS FOR MINIMUM-NORM FIXED POINTS OF PSEUDOCONTRACTIONS IN HILBERT SPACES. Taiwanese J. Math. 16 (2012), no. 4, 1489--1506. doi:10.11650/twjm/1500406745. https://projecteuclid.org/euclid.twjm/1500406745


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