• 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.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.881-893
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• 1997

E. M. Silvia introduced the class $S^\lambda_\alpha$ of $\alpha$-spirallike functions f(z) satisfying the condition $$ (A) Re[(e^{i\lambda} - \alpha) \frac{zf'(z)}{f(z)} + \alpha \frac{(zf'(z))'}{f'(z)}] > 0, $$ where $\alpha \geq 0, $\mid$\lambda$\mid$ < \frac{\pi}{2}$ and $$\mid$z$\mid$ < 1$. We will generalize Silvia class of functions by formally replacing f(z) in the denominator of (A) by a spirallike function g(z). We denote the new class of functions by $Y(\alpha,\lambda)$. In this note we obtain some results for the class $Y(\alpha,\lambda)$ including integral representation formula, relations between our class $Y(\alpha,\lambda)$ and Ziegler class $Z_\lambda$, the radius of convexity problem, a few coefficient estimates and a covering theorem for the class $Y(\alpha,\lambda)$.

• 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.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.743-757
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• 2021

We consider a different version of Schwarz Lemma for λ-spirallike function of complex order at the boundary of the unit disc D. We estimate the modulus of the angular derivative of the function $\frac{zf^{\prime}(z)}{f(z)}$ from below for λ-spirallike function f(z) of complex order at the boundary of the unit disc D by taking into account the zeros of the function f(z)-z which are different from zero. We also estimate the same function with the second derivatives of the function f at the points z = 0 and z = z₀ ≠ 0. We show the sharpness of these estimates and present examples.

• 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.55 no.4
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• pp.953-967
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• 2015

In this article, by making use of a linear multiplier fractional differential operator $D^{{\delta},m}_{\lambda}$, we introduce a new subclass of spiral-like functions. The main object is to provide some subordination results for functions in this class. We also find sufficient conditions for a function to be in the class and derive Fekete-$Szeg{\ddot{o}}$ inequalities.