Delta-convexity with given weights
Abstract
Some differentiability results from the paper of D.Ş. Marinescu & M. Monea [7] on delta-convex mappings, obtained for real functions, are extended for mappings with values in a normed linear space. In this way, we are nearing the completion of studies established in papers [2], [5] and [7].
Keywords
delta convexity; Jensen delta convexity; delta (s,t)-convexity; functional inequalities; absolute continuity; Radon-Nikodym property (RNP)
References
2. N. Bourbăcuţ, Problem 11641, Amer. Math. Monthly 119 (2012), no. 4, p. 345.
3. N. Dunford and B.J. Pettis, Linear operations on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323–392.
4. R. Ger, Stability aspects of delta-convexity, in: Th.M. Rasssias, J. Tabor (eds.), Stability of Mappings of Hyers-Ulam Type, Hadronic Press, Palm Harbor, 1994, pp. 99–109.
5. R. Ger, A Functional Inequality, Solution of Problem 11641, Amer. Math. Monthly 121 (2014), no. 2, 174–175.
6. N. Kuhn, On the structure of (s,t)-convex functions, in: W. Walter (ed.), General Inequalities. 5. Proceedings of the Fifth International Conference held in Oberwolfach, May 4-10, 1986, International Series of Numerical Mathematics, 80, Birkhäuser Verlag, Basel, 1987, pp. 161–174.
7. D.Ş. Marinescu and M. Monea, An extension of a Ger’s result, Ann. Math. Sil. 32 (2018), 263–274.
8. A. Olbryś, A support theorem for delta (s,t)-convex mappings, Aequationes Math. 89 (2015), no. 3, 937–948.
9. R.S. Phillips, On weakly compact subsets of a Banach space, Amer. J. Math. 65 (1943), 108–136.
10. L. Veselý and L. Zajíček, Delta-convex Mappings Between Banach Spaces and Applications, Dissertationes Math. (Rozprawy Mat.) 289, Polish Scientific Publishers, Warszawa, 1989.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
https://orcid.org/0000-0001-6988-5415
The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.
- License
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license. - Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. - User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor. - Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
