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NOTES ON GRAPH-CONVERGENCE FOR MAXIMAL MONOTONE OPERATORS

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  26 November 2010

FILOMENA CIANCIARUSO ,
GIUSEPPE MARINO ,
LUIGI MUGLIA  and
HONG-KUN XU
FILOMENA CIANCIARUSO
Affiliation:
Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende (CS), Italy (email: cianciaruso@unical.it)
GIUSEPPE MARINO
Affiliation:
Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende (CS), Italy (email: gmarino@unical.it)
LUIGI MUGLIA
Affiliation:
Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende (CS), Italy (email: muglia@mat.unical.it)
HONG-KUN XU*
Affiliation:
Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan Department of Mathematics, College of Science, King Saud University, PO Box 2455, Riyadh 11451, Saudi Arabia (email: xuhk@math.nsysu.edu.tw)
*
✉For correspondence; e-mail: xuhk@math.nsysu.edu.tw
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Abstract

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We construct a sequence {An} of maximal monotone operators with a common domain and converging, uniformly on bounded subsets, to another maximal monotone operator A; however, the sequence {t−1nAn} fails to graph-converge for some null sequence {tn}.

Keywords

maximal monotone operatorgraph-convergenceMann iteration

MSC classification

Secondary: 47H05: Monotone operators and generalizations 47H10: Fixed-point theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 1 , February 2011 , pp. 22 - 29
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The second author was supported in part by Ministero dell’Universitá e della Ricerca of Italy. The fourth author was supported in part by NSC 97-2628-M-110-003-MY3.

References

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