Converse Ohlin’s lemma for convex and strongly convex functions

• Autorzy: Adamek Mirosław , Nikodem Kazimierz

Identyfikatory

DOI

10.1515/jaa-2022-2011

• Języki publikacji: EN

Abstrakty

EN

Theorems which are converse to the Ohlin lemma for convex and strongly convex functions are proved. New proofs of probabilistic characterizations of convex and strongly convex functions are presented.

Słowa kluczowe

EN

converse Ohlin’s lemma; convex functions; strongly convex functions

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 1
• Strony: 123--126
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Adamek Mirosław

• Department of Mathematics, University of Bielsko-Biala, ul. Willowa 2, 43-309 Bielsko-Biała, Poland

• https://orcid.org/0000-0002-9268-8951

autor

Nikodem Kazimierz

• Department of Mathematics, University of Bielsko-Biala, ul. Willowa 2, 43-309 Bielsko-Biała, Poland

• https://orcid.org/0000-0001-9458-2272

Bibliografia

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• [2] M. Denuit, C. Lefevre and M. Shaked, The s-convex orders among real random variables, with applications, Math. Inequal. Appl. 1 (1998), no. 4, 585-613.
• [3] M. Klaričić Bakula and K. Nikodem, On the converse Jensen inequality for strongly convex functions, J. Math. Anal. Appl. 434 (2016), no. 1, 516-522.
• [4] N. Merentes and K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010), no. 1-2, 193-199.
• [5] K. Nikodem, On strongly convex functions and related classes of functions, in: Handbook of Functional Equations, Springer Optim. Appl. 95, Springer, New York (2014), 365-405.
• [6] K. Nikodem and T. Rajba, Ohlin and Levin-Stečkin-type results for strongly conve functions, Ann. Math. Sil. 34 (2020), no. 1, 123-132.
• [7] J. Ohlin, On a class of measures of dispersion with application to optimal reinsurance, Astin Bull. 5 (1969), 249-266.
• [8] A. Olbryś and T. Szostok, Inequalities of the Hermite-Hadamard type involving numerical differentiation formulas, Results Math. 67 (2015), no. 3-4, 403-416.
• [9] B. T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl. 7 (1966), 72-75.
• [10] T. Rajba, On the Ohlin lemma for Hermite-Hadamard-Fejér type inequalities, Math. Inequal. Appl. 17 (2014), no. 2, 557-571.
• [11] T. Rajba, On some recent applications of stochastic convex ordering theorems to some functional inequalities for convex functions: A survey, in: Developments in functional equations and related topics, Springer Optim. Appl. 124, Springer, Cham (2017), 231-274.
• [12] T. Rajba and S. Wąsowicz, Probabilistic characterization of strong convexity, Opuscula Math. 31 (2011), no. 1, 97-103.
• [13] A. W. Roberts and D. E. Varberg, Convex Functions, Pure Appl. Math. 57, Academic Press, New York, 1973.
• [14] T. Szostok, Ohlin’s lemma and some inequalities of the Hermite-Hadamard type, Aequationes Math. 89 (2015), no. 3, 915-926.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).