Preserving maximal monotonicity with applications in sum and composition rules |
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Authors: | Mohsen Alimohammady Vahid Dadashi |
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Institution: | 1. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, 47416-95447, Iran 2. Department of Mathematics, Islamic Azad University–Sari Branch, Sari, Iran
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Abstract: | In this paper, we study maximal monotonicity preserving mappings on the Banach space X × X *. Indeed, for a maximal monotone set ${M \subset X\times X^*}$ and for a multifunction ${T: X \times X^* \multimap Y \times Y^*}$ , under some sufficient conditions on M and T we show that T(M) is maximal monotone. As two consequences of this result we get sum and composition rules for maximal monotone operators. |
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