• 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.58 no.2
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• pp.257-270
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• 2018

The well-known theory of differential subordination developed by Miller and Mocanu is applied to obtain several inclusions between $Carath{\acute{e}}odory$ functions and starlike functions. These inclusions provide sufficient conditions for normalized analytic functions to belong to certain class of Ma-Minda starlike functions.

• East Asian mathematical journal
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• v.17 no.2
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• pp.175-183
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• 2001

The main object of this paper is to investigate several majorization problems involving two subclasses $S_{p,q}(\gamma)$ and $C_{p,q}(\gamma)$ of p-valently starlike and p-valently convex functions of complex order ${\gamma}{\neq}0$ in the open unit disk $\mathbb{u}$. Relevant connections of the results presented here with those given by earlier workers on the subject are also indicated.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.227-242
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• 2019

In the present paper, we derive several sufficient conditions for $Carath{\acute{e}}odory$ functions in the open unit disk ${\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$ under the constraint that the second coefficient of the function is preassigned. And, we obtain some sufficient conditions for strongly starlike functions in ${\mathbb{D}}$.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.613-621
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• 2017

In this paper, we have constructed subclasses of bi-univalent functions associated with ${\lambda}$-bi-pseudo-starlike functions in the unit disc U. Furthermore we established bound on the coefficients for the subclasses $S^{\lambda}_{\Sigma}(k,{\alpha})$ and $S^{\lambda}_{\Sigma}(k,{\beta})$.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.123-130
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• 2005

In this paper we discuss a class of analytic functions related to the starlike functions in the unit disk. We prove that this class belongs to the class of close-to-convex functions, we obtain the sharp coefficient upper bounds and distortion theorem of this class, we also get the convexity radius of this class.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.71-81
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• 2021

The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.597-610
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• 2016

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.120-135
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• 2024

A normalized analytic function f, defined on the unit disk 𝔻, is starlike of reciprocal order α > 1 if the real part of f(z)/(zf'(z)) is less than α for all z ∈ 𝔻. By utilizing the theory of differential subordination, we establish several sufficient conditions for analytic functions defined on 𝔻 to be starlike of reciprocal order. Additionally, we investigate the conditions under which the function f(z)/(zf'(z)) is subordinate to the function 1 + (α - 1)z. This subordination, in turn, is sufficient for the function f to be starlike of reciprocal order α > 1.