• Honam Mathematical Journal
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• v.43 no.3
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• pp.503-511
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• 2021

In this present work, we obtain certain coefficients of the subclass 𝓗_λ,𝛄(s, b, n) of non-Bazilević functions and estimate the relevant connection to the famous classical Fekete-Szegö inequality of functions belonging to this class.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.587-599
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• 1996

We assume throughout the paper that f(z) is a conformal function in the ipen unit disk $D = {z : $\mid$z$\mid$ < 1}$. In the rest of paper, conformal means analytic and locally univalent.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.439-446
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• 2009

We consider the univalence function classes T, $T_2,\;T_{2,{\mu}}$, and S(p). For these classes we shall study some univalence properties for a general integral operator. Furthermore we shall extend some known univalence criteria, i.e., Becker-type criteria.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.659-666
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• 2014

Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}&gt;0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.467-478
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• 2013

The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes $V_H({\beta})$ and $U_H({\beta})$. Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.97-109
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• 2006

In this paper, the authors introduce new classes of p-valent functions defined by Dziok-Srivastava linear operator and the multiplier transformation and study their properties by using certain first order differential subordination and superordination. Also certain inclusion relations are established and an integral transform is discussed.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.949-965
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• 2021

The main focus of the present paper is to present new set of sufficient conditions so that the normalized form of the Mittag-Leffler and Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disk. Interesting consequences and examples are derived to support that these results are better than the existing ones and improve several results available in the literature.

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.1-12
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• 2013

The purpose of the present paper is to obtain some subordination- and superordination-preserving properties for multivalent function associated the differintegral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich type theorem for the integral operator is also considered.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.957-965
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• 2018

We study the class $C{\mathcal{V}} ({\Omega})$ of analytic functions f in the unit disk ${\mathbb{D}}=\{z{\in}{\mathbb{C}}$ : ${\mid}z{\mid}$ < 1} of the form $f(z)=z+{\sum}_{n=2}^{\infty}a_nz^n$ satisfying $$1+\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}{\in}{\Omega},\;z{\in}{\mathbb{D}}$$, where ${\Omega}$ is a convex and proper subdomain of $\mathbb{C}$ with $1{\in}{\Omega}$. Let ${\phi}_{\Omega}$ be the unique conformal mapping of $\mathbb{D}$ onto ${\Omega}$ with ${\phi}_{\Omega}(0)=1$ and ${\phi}^{\prime}_{\Omega}(0)$ > 0 and $$k_{\Omega}(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\exp}\({\displaystyle\smashmargin{2}{\int\nolimits_{0}}^t}{\zeta}^{-1}({\phi}_{\Omega}({\zeta})-1)d{\zeta}\)dt$$. Let $z_0,z_1{\in}{\mathbb{D}}$ with $z_0{\neq}z_1$. As the first result in this paper we show that the region of variability $\{{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0)\;:\;f{\in}C{\mathcal{V}}({\Omega})\}$ coincides wth the set $\{{\log}\;k^{\prime}_{\Omega}(z_1z)-{\log}\;k^{\prime}_{\Omega}(z_0z)\;:\;{\mid}z{\mid}{\leq}1\}$. The second result deals with the case when ${\Omega}$ is the right half plane ${\mathbb{H}}=\{{\omega}{\in}{\mathbb{C}}$ : Re ${\omega}$ > 0}. In this case $CV({\Omega})$ is identical with the usual normalized class of convex univalent functions on $\mathbb{D}$. And we derive the sharp upper bound for ${\mid}{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0){\mid}$, $f{\in}C{\mathcal{V}}(\mathbb{H})$. The third result concerns how far two functions in $C{\mathcal{V}}({\Omega})$ are from each other. Furthermore we determine all extremal functions explicitly.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.905-915
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• 2009

Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed.