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NOTES ON GRAPH-CONVERGENCE FOR MAXIMAL MONOTONE OPERATORS

Published online by Cambridge University Press:  26 November 2010

FILOMENA CIANCIARUSO
Affiliation:
Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende (CS), Italy (email: [email protected])
GIUSEPPE MARINO
Affiliation:
Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende (CS), Italy (email: [email protected])
LUIGI MUGLIA
Affiliation:
Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende (CS), Italy (email: [email protected])
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: [email protected])
*
For correspondence; e-mail: [email protected]
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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}.

Type
Research Article
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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