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The radius of convexity of particular functions and applications to the study of a second order differential inequality

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Abstract

In this paper we determine the radius of convexity of particular functions. The obtained results are used to deduce sharp estimates regarding functions which satisfy a second order differential subordination. A lemma regarding starlikeness that involves the notion of convolution is established, and is used in order to obtain a sharp starlikeness condition.

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References

  1. Á. Baricz, D.K. Dimitrov, I. Mező, “Radii of starlikeness and convexity of some q-Bessel functions”, arXiv:1409.0293, 2014.

    MATH  Google Scholar 

  2. Á. Baricz, N. Yamur, “Radii of convexity of some Lommel and Struve functions”, arXiv:1410.5217, 2014.

    Google Scholar 

  3. Á. Baricz, R. Szász, “Close-to-convexity of some special functions and their derivatives”, arXiv:1402.0692, 2014.

    MATH  Google Scholar 

  4. Á. Baricz, R. Szász, “The radius of convexity of normalized Bessel functions of the first kind”, Anal. Appl., 12 (5), 2014.

    Google Scholar 

  5. D.J. Hallenbeck, T.H. MacGregor, Linear Problems and Convexity Techniques in Geometric Function Theory (Pitman, Boston, 1984).

    MATH  Google Scholar 

  6. S.S. Miller, P.T. Mocanu, Differential Subordinations Theory and Applications (Marcel Dekker, New York, Basel 2000).

    MATH  Google Scholar 

  7. P.T. Mocanu, T. Bulboacă, G. Şt. Sălăgean, Teoria Geometricăa Funcţiilor Univalente (Casa Cărt¸ii de Ştiint¸ă, Cluj-Napoca, 2006).

    Google Scholar 

  8. St. Ruscheweyh, Convolutions in Geometric Function Theory (Presses de l’Universitéde Montréal, Montréal 1982).

    MATH  Google Scholar 

  9. R. Szász, “Inequalities in the complex plane”, J. of Inequal. Pure Appl.Math., 8 (1), 2007.

    Google Scholar 

  10. R. Szász, “About a differential inequality”, Acta Univ. Sapientiae Math., 1 (1), 87–93, 2009.

    MathSciNet  MATH  Google Scholar 

  11. R. Szász, “Geometric properties of the functions G and 1/G”, Math. Nachr., 288 (1), 115–120, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. Szász, “A sharp criterion for the univalence of Libera operator”, Creat.Math. Inf., 17 (1), 65–71, 2008.

    MathSciNet  MATH  Google Scholar 

  13. R. Szász, “Starlike image of a class of analytic functions”, Gen.Math., 16 (2), 59–67, 2008.

    MathSciNet  MATH  Google Scholar 

  14. R. Szász, “A sharp criterion for starlikeness”, Mathematica (Cluj), 48 (71), 89–98, 2006.

    MathSciNet  MATH  Google Scholar 

  15. R. Szász, “The sharp version of a criterion for starlikeness related to the operator of Alexander”, Ann. Polon. Math., 94 (1), 1–14, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  16. R. Szász, L. R. Albert, “About a condition for starlikeness”, J.Math. Anal. Appl., 335 (2), 1328–1334, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  17. R. Szász, Rezultate din teoria geometricăa funcţiilor (Editura Didacticăşi Pedagogică, Bucureşti, 2010).

    Google Scholar 

  18. R. Szász, “About the starlikeness of Bessel functions”, Integral Trans. Spec. Funct., 25 (9), 750–755, 2014.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Babeş-Bolyai University, Cluj-Napoca, Romania

    O. Engel & Á. O. Páll-Szabó

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  1. O. Engel
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  2. Á. O. Páll-Szabó
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Correspondence to O. Engel.

Additional information

Original Russian Text © O. Engel, A. O. Páll-Szabo, 2017, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2017, No. 3, pp. 16-29.

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Engel, O., Páll-Szabó, Á.O. The radius of convexity of particular functions and applications to the study of a second order differential inequality. J. Contemp. Mathemat. Anal. 52, 118–127 (2017). https://doi.org/10.3103/S1068362317030025

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  • DOI: https://doi.org/10.3103/S1068362317030025

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