• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1027-1041
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.165-173
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• 2018

In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^*({\alpha})$ of starlike functions of order ${\alpha}$ and $\mathcal{K}({\alpha}$) of convex functions of order ${\alpha}$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.92-108
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• 2023

We determine the upper bounds on fourth order Hankel determinants H⁽²⁾₄(f) and H⁽³⁾₄(f) for the class S^*_L of lemniscate starlike functions defined on the open unit disk which was introduced by Sokół and Stankiewicz in [17].

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.425-435
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• 2023

The classical Hardy Theorem on R states that a function f and its Fourier transform cannot be simultaneously very small; this fact was generalized by Miyachi in terms of L¹ + L^∞ and log⁺-functions. In this paper, we consider the k-Hankel transform, which is a deformation of the Hankel transform by a parameter k > 0 arising from Dunkl's theory. We study Miyachi's theorem for the k-Hankel transform on ℝ^d.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.437-444
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• 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.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.443-452
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.281-291
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• 2023

A normalized analytic function f is parabolic starlike if w(z) := zf' (z)/f(z) maps the unit disk into the parabolic region {w : Re w > |w - 1|}. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.481-491
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• 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.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.407-420
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• 2024

In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.699-715
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• 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.