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The equality case in some recent convexity inequalities

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EN
Abstrakty
EN
In this paper, we investigate a functional equation related to some recently introduced and investigated convexity type inequalities.
Rocznik
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269--277
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
autor
  • University of Debrecen Institute of Mathematics H-4010 Debrecen, Pf. 12, Hangary, maksa@math.klte.hu
Bibliografia
  • [1] P. Burai, A. Hazy, On Orlicz-convex functions, Proc. of the 12th Symposium of Mathematics and Its Applications, Editura Politechnica, Temesvar, (2010), 73–79.
  • [2] P. Burai, A. Hazy, Bernstein-Doetsch type results for generalized convex functions, Proc. of the 12th Symposium of Mathematics and Its Applications, Editura Politechnica, Temesvar, (2010), 118–124.
  • [3] P. Burai, A. Hazy, T. Juhasz, Bernstein-Doetsch type results for s-convex functions, Publ. Math. Debrecen 75 (2009) 1–2, 23-31.
  • [4] P. Burai, A. Hazy, On approximately h-convex functions, accepted for publication, Journal of Convex Analysis, available electronically http://www.heldermann.de/JCA/JCA18/JCA182/jca18029.htm.
  • [5] W.W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen, Publ. Inst. Math. (Beograd) 23 (1978), 13–20.
  • [6] W.W. Breckner, Hölder-continuity of certain generalized convex functions, Optimization 28 (1994), 201–209.
  • [7] G. Darboux, Sur la composition des forces en statique, Bull. Sci. Math. 9 (1875) 1, 281–288.
  • [8] Z. Daroczy, Notwendige und hinreichende Bedingungen für die Existenz von nichtkonstanten Lösungen linearer Funktionalgleichungen, Acta Sci. Math. (Szeged) 22 (1961), 31–41.
  • [9] Z. Daroczy, Zs. Pales, Convexity with given infinite weight sequences, Stochastica 11 (1987), 5–12.
  • [10] E.K. Godunova, V.I. Levin, Neravenstva dlja funkcii sirokogo klassa, soderzascego vypuklye, monotonnye i nekotorye drugie vidy funkii, Vycislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskva, 1985, pp. 138–142.
  • [11] A. Hazy, Bernstein-Doetsch type results for h-convex functions, accepted for publication, Math. Ineq. Appl. (2011).
  • [12] H. Hudzik, L. Maligranda, Some remarks on si-convex functions, Aequationes Math. 48 (1994), 100–111.
  • [13] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Prace Naukowe Uniwersytetu Śląskiego w Katowicach Vol. CDLXXXIX (Państwowe Wydawnictwo Naukowe – Uniwersytet Śląski, Warszawa–Krakow–Katowice, 1985).
  • [14] N. Kuhn, A note on t–convex functions, General Inequalitis 4, Internat. Ser. Numer. Math. 71 (1984), 269–276.
  • [15] N. Kuhn, On the structure of (s, t)-convex functions, General Inequalitis 5, Internat. Ser. Numer. Math. 80 (1987), 161–174.
  • [16] J. Matkowski, M. Pycia, On (α, a)-convex functions, Arch. Math (Basel) 64 (1995), 132–138.
  • [17] W. Orlicz, A note on modular spaces I, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 9 (1961), 157–162.
  • [18] C.E.M. Pearce, A.M. Rubinov, P-functions, quasi-convex functions and Hadamard-type inequalities, J. Math. Anal. Appl. 240 (1999), 92–104.
  • [19] F. Rado, J.A. Baker, Pexider’s equation and aggregation of allocations, Aequationes Math. 32 (1987), 227–239.
  • [20] J. Ratz, On the homogeneity of additive mappings, Aequationes Math. 14 (1976), 67–71.
  • [21] A.W. Roberts, D.E. Varberg, Convex Functions, Academic Press, New York, 1973.
  • [22] H. Steinhaus, Sur les distances des points des ensambles de mesure positive, Fund. Math. 1 (1920), 99–104.
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  • [24] S. Varošanec, On h-convexity, J. Math. Anal. Appl. 32 (2007), 303–311.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0005-0007
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