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Some Remarks on the Class of Continuous (Semi-) Strictly Quasiconvex Functions

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We introduce the notion of variational (semi-) strict quasimonotonicity for a multivalued operator T  : XX * relative to a nonempty subset A of X which is not necessarily included in the domain of T. We use this notion to characterize the subdifferentials of continuous (semi-) strictly quasiconvex functions. The proposed definition is a relaxation of the standard definition of (semi-) strict quasimonotonicity, the latter being appropriate only for operators with nonempty values. Thus, the derived results are extensions to the continuous case of the corresponding results for locally Lipschitz functions.

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Correspondence to A. Daniilidis.

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Communicated by S. Schaible.

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Daniilidis, A., Garcia Ramos, Y. Some Remarks on the Class of Continuous (Semi-) Strictly Quasiconvex Functions. J Optim Theory Appl 133, 37–48 (2007). https://doi.org/10.1007/s10957-007-9182-4

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