• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.231-242
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• 2018

We derive sharp upper bound on the initial coefficients and Hankel determinants for normalized analytic functions belonging to a class, introduced by Silverman, defined in terms of ratio of analytic representations of convex and starlike functions. A conjecture related to the coefficients for functions in this class is posed and verified for the first five coefficients.

• Kyungpook Mathematical Journal
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• 제52권1호
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• pp.33-38
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• 2012

The purpose of the present paper is to investigate mapping properties of an integral operator in which we show that the function g defined by $$g(z)=\{\frac{c+{\alpha}}{z^c}{\int}_{o}^{z}t^{c-1}(D^nf)^{\alpha}(t)dt\}^{1/{\alpha}}$$. belongs to the class $S(A,B)$ if $f{\in}S(n,A,B)$.

• Korean Journal of Mathematics
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• 제29권2호
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• pp.395-407
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• 2021

By considering a certain univalent function that maps the unit disk 𝕌 onto a strip domain, we introduce new subclasses of analytic and p-valent functions and determine the coefficient bounds for functions belonging to these new classes. Relevant connections of some of the results obtained with those in earlier works are also provided.

• 대한수학회논문집
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• 제11권3호
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• pp.665-672
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• 1996

Let U denote the set of all Schwarzian derivatives $S_f$ of conformal function f in the unit disk D. We show that if $S_f$ is a local extreme point of U, then f cannot omit an open set. We also show that if $S_f \in U$ is an extreme point of the closed convex hull $\bar{co}U$ of U, then f cannot omit a set of positive area. The proof of this uses Nguyen's theorem.

• 대한수학회보
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• 제44권4호
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• pp.683-689
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• 2007

Let $\mathcal{B}$ be a certain Banach space consisting of analytic functions defined on a bounded domain G in the complex plane. Let ${\varphi}$ be an analytic polynomial or a rational function and let $M_{\varphi}$ denote the operator of multiplication by ${\varphi}$. Under certain condition on ${\varphi}$ and G, we characterize the commutant of $M_{\varphi}$ that is the set of all bounded operators T such that $TM_{\varphi}=M_{\varphi}T$. We show that $T=M_{\Psi}$, for some function ${\Psi}$ in $\mathcal{B}$.

• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.395-404
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• 2005

Let α be a complex number with 𝕽α > 0. Let the functions f and g be analytic in the unit disc E = {z : |z| < 1} and normalized by the conditions f(0) = g(0) = 0, f'(0) = g'(0) = 1. In the present article, we study the differential subordinations of the forms $${\alpha}{\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}+{\frac{zf^{\prime}(z)}{f(z)}}{\prec}{\alpha}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}}+{\frac{zg^{\prime}(z)}{g(z)}},\;z{\in}E,$$ and $${\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}{\prec}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}},\;z{\in}E.$$ As consequences, we obtain a number of sufficient conditions for star likeness of analytic maps in the unit disc. Here, the symbol ' ${\prec}$ ' stands for subordination

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.725-742
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• 2021

The aim of this article is to estimate the coefficient bounds of certain subclasses of analytic functions. We claim that this is a novel and unique effort in combining the coefficient functional along with the new domains and the probability distributions which have not been found or are available in the literature of coefficients bounds. Here the authors analyze these bounds in the special domains associated with exponential function and sine function. Further we obtain Fekete-Szegö inequalities for the defined subclasses of analytic functions defined through Poisson distribution series and Pascal distribution series.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제22권4호
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• pp.417-444
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• 2008

본 논문에서는 세 가지 관련된 분야의 연구를 통하여 우리나 대학 신입생들의 함수 개념을 조사하였다. 대학 신입생들은 함수를 어떻게 이해하고 있는가?; 인식론적 장애를 포함한 오 개념에는 어떤 것들이 있는가?; 함수 개념은 어떤 경로를 거쳐서 획득되는가? 등이다. 이와 함께 대학의 여러 분야에서 함수가 어떻게 정의되고 쓰이는지를 살펴보고, 미국의 교과서들에 나타난 함수 정의와 도입을 살펴보았다. 설문조사와 이들을 토대로 함수를 대응의 관점에서 도입하는 새로운 교육과정에 대하여 수직선 테스트의 도입을 포함한 몇 가지 제언을 하였다.

• 호남수학학술지
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• 제37권3호
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• pp.317-323
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• 2015

The purpose of the present paper is to study certain radii problems for the function $$f(z)=\[{\frac{z^{1-{\gamma}}}{{\gamma}+{\beta}}}\(z^{\gamma}[D^nF(z)]^{\beta}\)^{\prime}\]^{1/{\beta}}$$, where ${\beta}$ is a positive real number, ${\gamma}$ is a complex number such that ${\gamma}+{\beta}{\neq}0$ and the function F(z) varies various subclasses of analytic functions with fixed second coefficients. Relevant connections of the results presented herewith various well-known results are briefly indicated.

• 대한수학회논문집
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• 제37권2호
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• pp.455-472
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• 2022

For j = 0, 1, 2,…, k - 1; k ≥ 2; and - 1 ≤ B < A ≤ 1, we have introduced the functions classes denoted by ST_[j,k](A, B) and K_[j,k](A, B), respectively, called the generalized (j, k)-symmetric starlike and convex functions. We first proved the sharp bounds on |f(z)| and |f'(z)|. Various radii related problems, such as radius of (j, k)-symmetric starlikeness, convexity, strongly starlikeness and parabolic starlikeness are determined. The quantity |a²₃ - a₅|, which provide the initial bound on Zalcman functional is obtained for the functions in the family ST_[j,k]. Furthermore, the sharp pre-Schwarzian norm is also established for the case when f is a member of K_[j,k](α) for all 0 ≤ α < 1.