Enlargements of Monotone Operators Determined by Representing Functions

Authors

  • Mahboubeh Rezaei

DOI:

https://doi.org/10.30495/jme.v6i0.93

Keywords:

Maximal monotone operators, ε-subdifferential, lower semicontinuous function, Fitzpatrick function, enlargement of an operator.

Abstract

In this paper, we study a new enlargement of subdifferential for any proper lower semicontinuous function. We know that ε-subdifferential of any proper lower semicontinuous function is an enlargement of its subfifferential and any point from the graph of ε-subdifferential can be approximated by a point from the graph of sub- fifferential. This nice property, apart from its theoretical importance, gives also the possibility to use the enlargement of subdifferentials in finding approximate solutions of inclusions determined by subdifferentials. We define a new enlargement and observe, in the case subdiffer- entials, the relation between this new enlargement and the ε-subdiffer- ential.

Author Biography

Mahboubeh Rezaei

Department of Mathematics Assistant Professor of Mathematics University of Isfahan P.O. Box 81745-163 Isfahan, Iran

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Published

2012-06-01

Issue

Vol. 6

Section

Vol. 6, No. 1, (2012)

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