Abstract
In this paper, we examine properties of topical (increasing and plus-homogeneous) functions defined on a normed linear space \({X}\). We also study many results of abstract convexity such as support set, polarity and subdifferential set of these functions. Finally, we give a characterization for topical functions with respect to closed downward sets.
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Acknowledgments
The authors are very grateful to the anonymous referee for his/her useful suggestions on an earlier version of this paper. These suggestions have enabled the authors to improve the paper significantly. This research was supported partially by Graduate University of Advanced Technology and Mahani Mathematical Research Center.
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Mohebi, H., Samet, M. Abstract convexity of topical functions. J Glob Optim 58, 365–375 (2014). https://doi.org/10.1007/s10898-013-0037-2
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DOI: https://doi.org/10.1007/s10898-013-0037-2