• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.411-417
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• 2011

In the present paper, we are concerned with subordination problems related to ${\lambda}$-Robertson function. The radii of ${\lambda}$-spirallikeness and starlikeness of ${\lambda}$-Robert function are also determined.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.277-291
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• 2019

Using the concept of bounded boundary rotation, we investigate various properties of two new generalized classes of spirallike and Robertson functions of complex order with bounded boundary rotations.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.681-689
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• 2018

In this paper, we defined new subclasses of Spirallike and Robertson functions by using concept of q-derivative operator. We investigate convolution properties and coefficient estimates for both classes q-Spirallike and q-Robertson functions denoted by ${\mathcal{S}}^{\lambda}_q[A,\;B]$ and ${\mathcal{C}}^{\lambda}_q[A,\;B]$, respectively.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.1-16
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• 1996

Earlier in 1935[12], M. S. Robertson introduced the class of quadrant preserving functions. More precisely, let Q be the class of all functions f(z) analytic in the unit disk $D = {z : $\mid$z$\mid$ < 1}$ such that f(0) = 0, f'(0) = 1, and the range f(z) is in the j-th quadrant whenever z is in the j-th quadrant of D, j = 1,2,3,4. This class Q contains the subclass of normalized, odd univalent functions which have real coefficients. On the other hand, this class Q is contained in the class T of odd typically real functions which was introduced by W. Rogosinski [13]. Clearly, if $f \in Q$, then f(z) is real when z is real and therefore the coefficients of f are all real. Recently, it was observed by Y. Abu-Muhanna and T. H. MacGregor [1] that any function $f \in Q$ is odd. Instead of functions "preserving quadrants", the authors [1] have introduced the notion of "preserving sectors".

• Honam Mathematical Journal
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• v.3 no.1
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• pp.167-173
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• 1981

본(本) 논문(論文)은 M. S. Robertson이 만든 함수족(函數族) G(0, 2)에 대(對)한 변분공식(變分公式)(1, 3)을 확장하여 함수족(函數族) $G(\alpha, k)$, $$(\mid\alpha\mid<\frac{\pi}{2},\;k{\geq_-}2)$$에 적용이 되는 새 변분공식(變分公式) (2.18)을 유도하고, 그것을 증명하였다. 그 증명과정(證明過程)은 Schiffer나 Hummel의 방법(方法)을 사용(使用)하지 않고, Poisson-Stieltijes 적분공식(積分公式)을 이용(利用)하여 새로운 방법(方法)으로 증명하는 데 성공(成功)하였다.

• Journal of The Korean Astronomical Society
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• v.27 no.2
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• pp.103-117
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• 1994

To extend the work of Gott, Park, and Lee (1989), statistical properties of gravitational lensing in a wide variety of cosmological models involving non-zero cosmological constant is investigated, using the redshifts of both lens and source and observed angular separation of images for gravitational lens systems. We assume singular isothermal sphere as lensing galaxy in homogenous and isotropic Friedmann­Lemaitre-Robertson- Walker universe, Schechter luminosity function, standard angular diameter distance formula and other galaxy parameters used in Fukugita and Turner (1991). To find the most adequate flat cosmological model and put a limit on the value of dimensionless cosmological constant $\lambda_0$, the mean value of the angular separation of images, probability distribution of angular separation and cumulative probability are calculated for given source and lens redshifts and compared with the observed values through several statistical methods. When there is no angular selection effect, models with highest value of $\lambda_0$ is preferred generally. When the angular selection effects are considered, the preferred model depends on the shape of the selection functions and statistical methods; yet, models with large $\lambda_0$ are preferred in general. However, the present data can not rule out any of the flat universe models with enough confidence. This approach can potentially select out best model. But at the moment, we need more data.