Delta-Convexity With Given Weights

Ger, Roman

doi:10.2478/amsil-2020-0003

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Delta-Convexity With Given Weights

Annales Mathematicae Silesianae

Volume 34 (2020): Issue 1 (July 2020)

By: Roman Ger

Open Access

|May 2020

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].

References

[1] Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis, American Mathematical Society, Colloquium Publications, 48, American Mathematical Society, Providence, 2000.10.1090/coll/048
Search in Google Scholar Back to article
[2] N. Bourbăcuţ, Problem 11641, Amer. Math. Monthly 119 (2012), no. 4, p. 345.
Search in Google Scholar Back to article
[3] N. Dunford and B.J. Pettis, Linear operations on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323–392.10.1090/S0002-9947-1940-0002020-4
Search in Google Scholar Back to article
[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.
Search in Google Scholar Back to article
[5] R. Ger, A Functional Inequality, Solution of Problem 11641, Amer. Math. Monthly 121 (2014), no. 2, 174–175.
Search in Google Scholar Back to article
[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.
Search in Google Scholar Back to article
[7] D.Ş. Marinescu and M. Monea, An extension of a Ger’s result, Ann. Math. Sil. 32 (2018), 263–274.
Search in Google Scholar Back to article
[8] A. Olbryś, A support theorem for delta (s, t)-convex mappings, Aequationes Math. 89 (2015), no. 3, 937–948.
Search in Google Scholar Back to article
[9] R.S. Phillips, On weakly compact subsets of a Banach space, Amer. J. Math. 65 (1943), 108–136.10.2307/2371776
Search in Google Scholar Back to article
[10] L. Veselý and L. Zajíček, Delta-convex Mappings Between Banach Spaces and Applications, Dissertationes Math. (Rozprawy Mat.) 289, Polish Scientific Publishers, Warszawa, 1989.
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/amsil-2020-0003 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 73 - 80

Submitted on: Nov 8, 2019

Accepted on: Mar 6, 2020

Published on: May 8, 2020

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

delta convexity,

Jensen delta convexity,

delta ()-convexity,

functional inequalities,

absolute continuity,

Radon-Nikodym property (RNP)

Related subjects:

Mathematics,

General mathematics

© 2020 Roman Ger, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

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