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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Alimohammady, M., Dadashi, V. Preserving maximal monotonicity with applications in sum and composition rules. Optim Lett 7, 511–517 (2013). https://doi.org/10.1007/s11590-011-0435-7
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DOI: https://doi.org/10.1007/s11590-011-0435-7