• 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.19 no.1
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• pp.97-105
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• 1997

Let $R_k({\alpha})$, $0{\leq}{\alpha}<1$, $k{\geq}2$ denote certain subclasses of analytic functions in the unit disc E with bounded radius rotation. A function f, analytic in E and given by $f(z)=z+{\sum_{m=2}^{\infty}}a_m{z^m}$, is said to be in the family $R_k(n,{\alpha})n{\in}N_o=\{0,1,2,{\cdots}\}$ and * denotes the Hadamard product. The classes $R_k(n,{\alpha})$ are investigated and same properties are given. It is shown that $R_k(n+1,{\alpha}){\subset}R_k(n,{\alpha})$ for each n. Some integral operators defined on $R_k(n,{\alpha})$ are also studied.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.995-1007
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• 2022

In this article, we initiate subclasses of functions with boundary and radius rotations that are related to limaçon domains and examine some of their geometric properties. Radius results associated with functions in these classes and their linear combination are studied. Furthermore, the growth rate of coefficients, arc length and coefficient estimates are derived for these novel classes. Overall, some useful consequences of our findings are also illustrated.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.449-461
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• 2001

The purpose of this paper is to study several geometric properties for the new class $G_{\kappa}(\beta)$ including geometric interpretation, coefficient estimates, radius of convexity, distortion property and covering theorem.