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Licensed Unlicensed Requires Authentication Published by De Gruyter October 20, 2018

Some results on abstract convexity of functions

Hossein Mohebi and Hasan Barsam
From the journal Mathematica Slovaca

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.

  1. Communicated by Ján Borsík

References

[1] Barsam, H.—Mohebi, H.: Characterizations of upward and downward sets in semimodules by using topical functions, Numer. Funct. Anal. Optim. 37(11) (2016), 1354–1377.10.1080/01630563.2016.1193518Search in Google Scholar

[2] Doagooei, A. R.: Sub-topical functions and plus-co-radiant set, Optimization 65 (2014), 107–119.10.1080/02331934.2014.994629Search in Google Scholar

[3] Doagooei, A. R.—Mohebi, H.: Optimization of the difference of topical functions, J. Global Optim. 57 (2013), 1349–1358.10.1007/s10898-012-9991-3Search in Google Scholar

[4] Mohebi, H.: Topical functions and their properties in a class of ordered Banach spaces, Contin. Optim. 99 (2005), 343–360.10.1007/0-387-26771-9_12Search in Google Scholar

[5] Mohebi, H.—Sadeghi, H.: Monotonic analysis over ordered topological vector spaces: I, Optimization 56 (3) (2007), 305–321.10.1080/02331930600819746Search in Google Scholar

[6] Mohebi, H.—Samet, M.: Abstract convexity of topical functions, J. Global Optim. 58 (2014), 365–375.10.1007/s10898-013-0037-2Search in Google Scholar

[7] Rubinov, A. M.: Abstract Convexity and Global Optimization, Kluwer Acad. Publ./Ister, Boston, Dordrecht, London, 2000.10.1007/978-1-4757-3200-9Search in Google Scholar

[8] Rubinov, A. M.—Singer, I.: Topical and sub-topical functions, downward sets and abstract convexity, Optimization 50 (2001), 307–351.10.1080/02331930108844567Search in Google Scholar

[9] Singer, I.: On radiant sets, downward sets, topical functions and sub-topical functions in lattice ordered groups, Optimization 53 (2004), 393–428.10.1080/02331930412331282418Search in Google Scholar

Received: 2016-11-07
Accepted: 2017-08-08
Published Online: 2018-10-20
Published in Print: 2018-10-25

© 2018 Mathematical Institute Slovak Academy of Sciences