Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  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  show that T(M) is maximal monotone. As two consequences of this result  get sum and composition rules for maximal monotone operators.
['Mohsen Alimohammady', 'Vahid Dadashi']
I am writing a research paper on a idea Preserving maximal monotonicity with applications in sum and composition rules
[{"from": "human", "value": "I am writing a research paper on a idea Preserving maximal monotonicity with applications in sum and composition rules"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study maximal monotonicity preserving mappings on the Banach space X \u00d7 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  show that T(M) is maximal monotone. As two consequences of this result  get sum and composition rules for maximal monotone operators."}]