Abstract: In this talk we will discuss some results about quasimonotone family of operators. For some notions that are extensions of monotoniticity but not beyond quasimonotonicity like pseudomonotonicity, semistrict quasimonotonicity, strict quasimonotonicity and proper quasimonotonicity, we will discuss systematically when the sum of two operators satisfying one of those properties, inherits the same property. Several examples showing the optimality in some sense of our results, are presented. Join work with: Fabián Flores-Bazán and Nicolas Hadjisavvas.
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