A new condition for maximal monotonicity via representative functions |
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Authors: | Radu Ioan Boţ,Ernö Robert Csetnek,Gert Wanka |
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Affiliation: | Faculty of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany |
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Abstract: | In this paper we give a weaker sufficient condition for the maximal monotonicity of the operator S+A∗TA, where S:X?X∗, T:Y?Y∗ are two maximal monotone operators, A:X→Y is a linear continuous mapping and X,Y are reflexive Banach spaces. We prove that our condition is weaker than the generalized interior-point conditions given so far in the literature. This condition is formulated using the representative functions of the operators involved. In particular, we rediscover some sufficient conditions given in the past using the so-called Fitzpatrick function for the maximal monotonicity of the sum of two maximal monotone operators and for the precomposition of a maximal monotone operator with a linear operator, respectively. |
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Keywords: | 47H05 46N10 42A50 |
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