• Title, Summary, Keyword: Hankel determinant

Search Result 18, Processing Time 0.025 seconds

SHARPENED FORMS OF ANALYTIC FUNCTIONS CONCERNED WITH HANKEL DETERMINANT

  • Ornek, Bulent Nafi
    • Korean Journal of Mathematics
    • /
    • v.27 no.4
    • /
    • pp.1027-1041
    • /
    • 2019
  • In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Jack's lemma and Hankel determinant were used. We will get a sharp upper bound for Hankel determinant H2(1). Also, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

UPPER BOUND ON THE THIRD HANKEL DETERMINANT FOR FUNCTIONS DEFINED BY RUSCHEWEYH DERIVATIVE OPERATOR

  • Yavuz, Tugba
    • Communications of the Korean Mathematical Society
    • /
    • v.33 no.2
    • /
    • pp.437-444
    • /
    • 2018
  • Let S denote the class of analytic and univalent functions in the open unit disk $D=\{z:{\mid}z{\mid}<1\}$ with the normalization conditions f(0) = 0 and f'(0) = 1. In the present article, an upper bound for third order Hankel determinant $H_3(1)$ is obtained for a certain subclass of univalent functions generated by Ruscheweyh derivative operator.

Fekete-Szegö Problem and Upper Bound of Second Hankel Determinant for a New Class of Analytic Functions

  • Bansal, Deepak
    • Kyungpook Mathematical Journal
    • /
    • v.54 no.3
    • /
    • pp.443-452
    • /
    • 2014
  • In the present investigation we consider Fekete-Szeg$\ddot{o}$ problem with complex parameter ${\mu}$ and also find upper bound of the second Hankel determinant ${\mid}a_2a_4-a^2_3{\mid}$ for functions belonging to a new class $S^{\tau}_{\gamma}(A,B)$ using Toeplitz determinants.

UPPER BOUND OF SECOND HANKEL DETERMINANT FOR A SUBCLASS OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER

  • Mustafa, Nizami
    • Communications of the Korean Mathematical Society
    • /
    • v.34 no.3
    • /
    • pp.783-797
    • /
    • 2019
  • In this paper, we introduce and investigate a subclass ${\Im}_{\Sigma}({\alpha},{\beta},{\gamma})$ of analytic and bi-univalent functions of complex order in the open unit disk U in complex plane. Here, we obtain an upper bound for the second Hankel determinant of the functions belonging to this class. Moreover, several interesting conclusions of the results obtained here are also discussed.

BOUNDS OF HANKEL DETERMINANTS FOR ANALYTIC FUNCTION

  • Ornek, Bulent Nafi
    • Korean Journal of Mathematics
    • /
    • v.28 no.4
    • /
    • pp.699-715
    • /
    • 2020
  • In this paper, we give estimates of the Hankel determinant H2(1) in a novel class 𝓝 (𝜀) of analytical functions in the unit disc. In addition, the relation between the Fekete-Szegö function H2(1) and the module of the angular derivative of the analytical function p(z) at a boundary point b of the unit disk will be given. In this association, the coefficients in the Hankel determinant b2, b3 and b4 will be taken into consideration. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

Some Coefficient Inequalities Related to the Hankel Determinant for a Certain Class of Close-to-convex Functions

  • Sun, Yong;Wang, Zhi-Gang
    • Kyungpook Mathematical Journal
    • /
    • v.59 no.3
    • /
    • pp.481-491
    • /
    • 2019
  • In the present paper, we investigate the upper bounds on third order Hankel determinants for certain class of close-to-convex functions in the unit disk. Furthermore, we obtain estimates of the Zalcman coefficient functional for this class.

THIRD ORDER HANKEL DETERMINANT FOR CERTAIN UNIVALENT FUNCTIONS

  • BANSAL, DEEPAK;MAHARANA, SUDHANANDA;PRAJAPAT, JUGAL KISHORE
    • Journal of the Korean Mathematical Society
    • /
    • v.52 no.6
    • /
    • pp.1139-1148
    • /
    • 2015
  • The estimate of third Hankel determinant $$H_{3,1}(f)=\left|a_1\;a_2\;a_3\\a_2\;a_3\;a_4\\a_3\;a_4\;a_5\right|$$ of the analytic function $f(z)=z+a2z^2+a3z^3+{\cdots}$, for which ${\Re}(1+zf^{{\prime}{\prime}}(z)/f^{\prime}(z))>-1/2$ are investigated. The corrected version of a known results [2, Theorem 3.1 and Theorem 3.3] are also obtained.

UPPER BOUNDS OF SECOND HANKEL DETERMINANT FOR UNIVERSALLY PRESTARLIKE FUNCTIONS

  • Ahuja, Om;Kasthuri, Murugesan;Murugusundaramoorthy, Gangadharan;Vijaya, Kaliappan
    • Journal of the Korean Mathematical Society
    • /
    • v.55 no.5
    • /
    • pp.1019-1030
    • /
    • 2018
  • In [12,13] the researchers introduced universally convex, universally starlike and universally prestarlike functions in the slit domain ${\mathbb{C}}{\backslash}[1,{\infty})$. These papers extended the corresponding notions from the unit disc to other discs and half-planes containing the origin. In this paper, we introduce universally prestarlike generalized functions of order ${\alpha}$ with ${\alpha}{\leq}1$ and we obtain upper bounds of the second Hankel determinant ${\mid}a_2a_4-a^2_3{\mid}$ for such functions.

COEFFICIENT BOUNDS FOR INVERSE OF FUNCTIONS CONVEX IN ONE DIRECTION

  • Maharana, Sudhananda;Prajapat, Jugal Kishore;Bansal, Deepak
    • Honam Mathematical Journal
    • /
    • v.42 no.4
    • /
    • pp.781-794
    • /
    • 2020
  • In this article, we investigate the upper bounds on the coefficients for inverse of functions belongs to certain classes of univalent functions and in particular for the functions convex in one direction. Bounds on the Fekete-Szegö functional and third order Hankel determinant for these classes have also investigated.