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On generalized convex functions and generalized subdifferential II

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Abstract

We introduce and study the notion of the \(\left( \sigma ,y\right) \)-conjugate of a proper \(\sigma \)-convex function. Some relations between the \(\sigma \)-subdifferentials and the Clarke–Rockafellar subdifferential are established. Also, we present some results regarding the \(\sigma \)-monotonicity of the \(\sigma \)-subdifferential of a function and its \(\sigma \)-convexity. Moreover, we obtain some particular relationships between the \(\sigma \)-subdifferential and the \(\left( \sigma ,y\right) \)-conjugate.

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Acknowledgements

The author expresses his gratitude to Professor Nicolas Hadjisavvas for his many insightful comments, suggestions, discussions, and remarks, as well as Professor Oleg A. Prokopyev, Editor in chief of Optimization Letters. Also, I would like to thank the two referees for their valuable comments on the manuscript and their suggestions and corrections for improving the document. The research was in part supported by a grant from the Iran National Science Foundation (INSF) (No. 97024302).

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  1. Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, 45137-66731, Iran

    Mohammad Hossein Alizadeh

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  1. Mohammad Hossein Alizadeh
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Correspondence to Mohammad Hossein Alizadeh.

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Alizadeh, M.H. On generalized convex functions and generalized subdifferential II. Optim Lett 15, 2225–2240 (2021). https://doi.org/10.1007/s11590-020-01682-0

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  • DOI: https://doi.org/10.1007/s11590-020-01682-0

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