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2020 | 34 (1) | 123--132
Tytuł artykułu

Ohlin and Levin-Stečkin-Type Results for Strongly Convex Functions

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Counterparts of the Ohlin and Levin-Stečkin theorems for strongly convex functions are proved. An application of these results to obtain some known inequalities related with strongly convex functions in an alternative and unified way is presented. (original abstract)
Rocznik
Tom
Strony
123--132
Opis fizyczny
Twórcy
  • University of Bielsko-Biala, Poland
autor
  • University of Bielsko-Biala, Poland
Bibliografia
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  • V.I. Levin and S.B. Stečkin, Inequalities, Amer. Math. Soc. Transl. (2) 14 (1960), 1-29.
  • N. Merentes and K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010), 193-199.
  • C.P. Niculescu and L.-E. Persson, Convex Functions and their Applications. A Contemporary Approach, CMS Books in Mathematics, Vol. 23, Springer, New York, 2006.
  • M. Niezgoda, An extension of Levin-Stečkin's theorem to uniformly convex and superquadratic functions, Aequationes Math. 94 (2020), 303-321.
  • K. Nikodem, On strongly convex functions and related classes of functions, in: Th.M. Rassias (ed.), Handbook of Functional Equations. Functional Inequalities, Springer Optimization and Its Applications, Vol. 95, Springer, New York, 2014, Chpt. 16, pp. 365-405.
  • J. Ohlin, On a class of measures of dispersion with application to optimal reinsurance, ASTIN Bulletin 5 (1969), 249-266.
  • A. Olbryś and T. Szostok, Inequalities of the Hermite-Hadamard type involving numerical differentiation formulas, Results Math. 67 (2015), 403-416.
  • B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl. 7 (1966), 72-75.
  • T. Rajba, On the Ohlin lemma for Hermite-Hadamard-Fejér type inequalities, Math. Inequal. Appl. 17 (2014), 557-571.
  • T. Rajba, On some recent applications of stochastic convex ordering theorems to some functional inequalities for convex functions: a survey, in: J. Brzdęk, K. Ciepliński, Th.M. Rassias (eds.), Developments in Functional Equations and Related Topics, Springer Optimization and Its Applications, Vol. 124, Springer, Cham, 2017, Chpt. 11, pp. 231-274.
  • T. Rajba and Sz. Wąsowicz, Probabilistic characterization of strong convexity, Opuscula Math. 31 (2011), 97-103.
  • A.W. Roberts and D.E. Varberg, Convex Functions, Academic Press, New York-London, 1973.
  • T. Szostok, Ohlin's lemma and some inequalities of the Hermite-Hadamard type, Aequationes Math. 89 (2015), 915-926.
  • T. Szostok, Inequalities for convex functions via Stieltjes integral, Lith. Math. J. 58 (2018), 95-103.
  • T. Szostok, Levin Stečkin theorem and inequalities of the Hermite-Hadamard type, arXiv preprint. Available at arXiv:1411.7708v1.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171605393

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