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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 2

Issues

Second hankel determinat for certain analytic functions satisfying subordinate condition

Erhan Deniz / Levent Budak
Published Online: 2018-03-31 | DOI: https://doi.org/10.1515/ms-2017-0116

Abstract

In this paper, we introduce and investigate the following subclass

1+1γzf(z)+λz2f(z)λzf(z)+(1λ)f(z)1φ(z)0λ1,γC{0}

of analytic functions, φ is an analytic function with positive real part in the unit disk 𝔻, satisfying φ (0) = 1, φ '(0) > 0, and φ (𝔻) is symmetric with respect to the real axis. We obtain the upper bound of the second Hankel determinant | a2a4a32 | for functions belonging to the this class is studied using Toeplitz determinants. The results, which are presented in this paper, would generalize those in related works of several earlier authors.

MSC 2010: Primary 30C45; Secondary 30C80

Keywords: analytic functions; starlike functions; convex functions; Ma-Minda starlike functions; Ma-Minda convex functions; subordination; second Hankel determinant

References

  • [1]

    Ali, R. M.—Lee, S. K.—Ravichandran, V.—Supramaniam, S.: The Fekete-Szegö coefficient functional for transforms of analytic functions, Bull. Iranian Math. Soc. 35 (2009), 119–142.Google Scholar

  • [2]

    Cantor, D. G.: Power series with integral coefficients, Bull. Amer. Math. Soc. 69 (1963), 362–366.CrossrefGoogle Scholar

  • [3]

    Deniz, E.—çağlar, M.—Orhan, H.: The Fekete-Szegö problem for a class of analytic functions defined by Dziok-Srivastava operator, Kodai Math. J. 35 (2012), 439–462.CrossrefGoogle Scholar

  • [4]

    Duren, P. L.: Univalent Functions. Grundlehren Math. Wiss. 259, Springer, New York, 1983.Google Scholar

  • [5]

    Fekete, M.—Szegö, G.: Eine Bemerkung uber ungerade schlichte Funktionen, J. London Math. Soc. 8 (1933), 85–89.Google Scholar

  • [6]

    Grenander, U.—Szegö, G.: Toeplitz Forms and their Applications. California Monographs in Mathematical Sciences, Univ. California Press, Berkeley, 1958.Google Scholar

  • [7]

    Janteng, A.—Halim, S. A.—Darus, M.: Hankel determinant for starlike and convex functions, Int. J. Math. Anal. (Ruse) 1 (2007), 619–625.Google Scholar

  • [8]

    Kanas, S.—Darwish, H. E.: Fekete Szegö problem for starlike and convex functions of complex order, Appl. Math. Lett. 23 (2010), 777–782.CrossrefGoogle Scholar

  • [9]

    Lee, S. K.—Ravichandran, V.—Supramaniam, S.: Bounds for the second Hankel determinant of certain univalent functions, J. Inequal. Appl. (2013), 2013:281.CrossrefGoogle Scholar

  • [10]

    Ma, W. C.—Minda, D.: A unified treatment of some special classes of univalent functions. In: Proceedings of the Conference on Complex Analysis (Tianjin, 1992), Conf. Proc. Lecture Notes Anal. I, Int. Press, Cambridge, MA, pp. 157–169.Google Scholar

  • [11]

    Orhan, H.—Deniz, E.—Raducanu, D.: The Fekete Szegö problem for subclasses of analytic functions defined by a differential operator related to conic domains, Comput. Math. Appl. 59 (2010), 283–295.CrossrefGoogle Scholar

  • [12]

    Ravichandran, V.—Polatoğlu, Y.—Bolcal, M.—Şen, A.: Certain subclasses of starlike and convex functions of complex order, Hacettepe J. Math. Stat. 34 (2005), 9–15.Google Scholar

  • [13]

    Srivastava, H. M.—AltIntaŞ, O.—Serenbay, S. K.: Coefficient bounds for certain subclasses of starlike functions of complex order, Appl. Math. Lett. 24 (2011), 1359–1363.CrossrefGoogle Scholar

  • [14]

    Xu, Q.-H.—Gui, Y. C.—Srivastava, H. M.: Coefficient estimates for certain subclasses of analytic functions of complex order, Taiwanese J. Math. 15 (2011), 2377–2386.CrossrefGoogle Scholar

About the article


Received: 2015-11-20

Accepted: 2016-05-15

Published Online: 2018-03-31

Published in Print: 2018-04-25


Citation Information: Mathematica Slovaca, Volume 68, Issue 2, Pages 463–471, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0116.

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