• Honam Mathematical Journal
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• v.39 no.2
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• pp.233-245
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• 2017

In the present paper we introduce and investigate an interesting subclass ${\mathcal{K}}^{(k)}_s({\gamma},p) $ of analytic and p-valently close-to-convex functions in the open unit disk ${\mathbb{U}}$. For functions belonging to this class, we derive several properties as the inclusion relationships and distortion theorems. The various results presented here would generalize many known recent results.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.98-109
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• 2022

In the present paper, we prove the growth and distortion theorems for the spirallike functions class 𝓢_k(λ) related to boundary radius rotation, and by using the distortion result, we get an estimate for the Gaussian curvature of a minimal surface lifted by a harmonic function whose analytic part belongs to the class 𝓢_k(λ). Moreover, we determine and draw the minimal surface corresponding to the harmonic Koebe function.

• Honam Mathematical Journal
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• v.9 no.1
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• pp.71-76
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• 1987

Let M be a positive real number and c a complex numbcr such that $\left|c-1\right|<M{\leq}Re{c}$. Let $f,f(z)=z+a_{2}Z^{2}+...,$ be analytic and univalent in the unit disc. It is said to belong to the class S(c, M) if $\left|zf'(z)/f(z)-c\right|<M$ We find growth and rotation theorems for the class S(c, M).

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.563-569
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• 2005

In [2], Jahangiri studied the harmonic starlike functions of order $\alpha$, and he defined the class T$_{H}$($\alpha$) consisting of functions J = h + $\bar{g}$ where hand g are the analytic and the co-analytic part of the function f, respectively. In this paper, we introduce the class T$_{H}$($\alpha$, $\beta$) of analytic functions and prove various coefficient inequalities, growth and distortion theorems, radius of convexity for the function h, if the function J belongs to the classes T$_{H}$($\alpha$) and T$_{H}$($\alpha$, $\beta$).

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.589-599
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• 2023

The object of this study is to introduce a new subclass of univalent analytic functions on the open unit disk. This subclass is created by utilizing univalent analytic functions with negative coefficients. We first explore the specific properties that functions in this subclass must possess before examining their coefficient characterization. By applying this approach, we observe several fascinating features, including coefficient approximations, growth and distortion theorems, extreme points and a demonstration of the radius of starlikeness and convexity for functions belonging to this subclass.