• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.623-629
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• 2005

Inclusion relations under certain integral operators are proved for k-uniformly starlike functions. These results are also extended to k-uniformly convex, close-to-convex, and quasi-convex functions

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.993-1010
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• 2022

In this paper, we establish some radius results and inclusion relations for starlike functions associated with a petal-shaped domain.

• 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.

• 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 $S^{\lambda}_{\Sigma}(k,{\beta})$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1377-1387
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• 2013

Let $f$ be a harmonic mapping on the unit disc ${\Delta}$ in $\mathbb{C}$. We give some condition for $f$ to be a quasiconformal homeomorphism on ${\Delta}$ and to have a quasiconformal extension to the whole plane $\bar{\mathbb{C}}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order ${\alpha}{\in}(0,1)$.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.615-620
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• 2008

For analytic functions f(z) in the open unit disc $\mathbb{D}$, an operator $N_{\alpha}(f(z))$ relating with starlike functions is introduced. The object of the present paper is to discuss some properties of the operator $N_{\alpha}(f(z))$.

• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.291-301
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• 2000

We give sufficient coefficient conditions for a class of meromorphic univalent harmonic functions that are starlike of some order. Furthermore, it is shown that these conditions are also necessary when the coefficients of the analytic part of the function are positive and the coefficients of the co-analytic part of the function are negative. Extreme points, convolution and convex combination conditions for these classes are also determined. Fianlly, comparable results are given for the convex analogue.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.51-65
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• 2011

In the present paper sufficient conditions, in terms of hyper-geometric inequalities, are found so that the Hohlov operator preserves a certain subclass of close-to-convex functions (denoted by $R^{\tau}$ (A, B)) and transforms the classes consisting of k-uniformly convex functions, k-starlike functions and univalent starlike functions into $\cal{R}^{\tau}$ (A, B).