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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 5

Issues

Some results on abstract convexity of functions

Hossein Mohebi / Hasan Barsam
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0162

Abstract

In this paper, we study abstract convexity topical and sub-topical functions. We obtain some results on abstract convexity such as support set and subdifferential in view of new elementary functions. Indeed, first we show that the ICR and IR functions are dense in IPH functions then the topical function and sub-topical function on topological vector space by another elementary function is studied. These elementary functions lead to obtain similar results with easier proofs.

MSC 2010: Primary 26B25; Secondary 49N15; 06F20

Keywords: abstract convexity; topical function; sub-topical function; elementary function; support set; subdifferential

References

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    Doagooei, A. R.: Sub-topical functions and plus-co-radiant set, Optimization 65 (2014), 107–119.Google Scholar

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    Doagooei, A. R.—Mohebi, H.: Optimization of the difference of topical functions, J. Global Optim. 57 (2013), 1349–1358.Google Scholar

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    Mohebi, H.: Topical functions and their properties in a class of ordered Banach spaces, Contin. Optim. 99 (2005), 343–360.Google Scholar

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    Mohebi, H.—Sadeghi, H.: Monotonic analysis over ordered topological vector spaces: I, Optimization 56 (3) (2007), 305–321.Google Scholar

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    Mohebi, H.—Samet, M.: Abstract convexity of topical functions, J. Global Optim. 58 (2014), 365–375.Google Scholar

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    Rubinov, A. M.: Abstract Convexity and Global Optimization, Kluwer Acad. Publ./Ister, Boston, Dordrecht, London, 2000.Google Scholar

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    Rubinov, A. M.—Singer, I.: Topical and sub-topical functions, downward sets and abstract convexity, Optimization 50 (2001), 307–351.Google Scholar

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    Singer, I.: On radiant sets, downward sets, topical functions and sub-topical functions in lattice ordered groups, Optimization 53 (2004), 393–428.Google Scholar

About the article

Received: 2016-11-07

Accepted: 2017-08-08

Published Online: 2018-10-20

Published in Print: 2018-10-25


Communicated by Ján Borsík


Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1001–1008, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0162.

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