• 대한수학회보
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• 제56권4호
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• pp.911-927
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• 2019

Let $\mathscr{B}^{{\eta},{\mu}}_{p,n}\;({\alpha});\;({\eta},{\mu}{\in}{\mathbb{R}},\;n,\;p{\in}{\mathbb{N}})$ denote all functions f class in the unit disk ${\mathbb{U}}$ as $f(z)=z^p+\sum_{k=n+p}^{\infty}a_kz^k$ which satisfy: $$\|\[{\frac{f^{\prime}(z)}{pz^{p-1}}}\]^{\eta}\;\[\frac{z^p}{f(z)}\]^{\mu}-1\| <1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. And $\mathscr{M}^{{\eta},{\mu}}_{p,n}\;({\alpha})$ indicates all meromorphic functions h in the punctured unit disk $\mathbb{U}^*$ as $h(z)=z^{-p}+\sum_{k=n-p}^{\infty}b_kz^k$ which satisfy: $$\|\[{\frac{h^{\prime}(z)}{-pz^{-p-1}}}\]^{\eta}\;\[\frac{1}{z^ph(z)}\]^{\mu}-1\|<1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. In this paper several sufficient conditions for some classes of functions are investigated. The authors apply Jack's Lemma, to obtain this conditions. Furthermore, sufficient conditions for strongly starlike and convex p-valent functions of order ${\gamma}$ and type ${\beta}$, are also considered.

• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.379-385
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• 2008

Making use of a linear operator, we introduce certain subclass of meromorphically univalent functions in the punctured unit disk and study its properties including some inclusion results, coefficient and distortion problems. Our result generalize many results known in the literature.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권1호
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• pp.1-11
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• 2003

In this paper we derive some sufficient conditions for starlikeness and close-to-convexity of order ${\alpha}$ of meromorphic functions in the punctured unit disk.

• 대한수학회논문집
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• 제15권2호
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• pp.263-274
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• 2000

The object of the present paper is to obtain some argu-ment properties of certain mermorphic functions in the punctured open unit disk. Furthermore, we investigate their integral preserving properties in a sector.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.217-232
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• 2011

Differential subordination and superordination results are obtained for multivalent meromorphic functions associated with the Liu-Srivastava linear operator in the punctured unit disk. These results are derived by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.625-639
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• 2015

Differential subordinations and superordinations results are obtained for certain meromorphic functions in the punctured unit disk which are associated with an integral operator. These results are obtained by investigating appropriate classes of a dmissible functions. Sandwich-type results are also obtained.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.553-563
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• 2021

As hypergeometric meromorphic multivalent functions of the form $$L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)=\frac{1}{{\zeta}^{\rho}}+{\sum\limits_{{\kappa}=0}^{\infty}}{\frac{(\varpi)_{{\kappa}+2}}{{(\sigma)_{{\kappa}+2}}}}\;{\cdot}\;{\frac{({\rho}-({\kappa}+2{\rho})t)}{{\rho}}}{\alpha}_{\kappa}+_{\rho}{\zeta}^{{\kappa}+{\rho}}$$ contains a new subclass in the punctured unit disk ${\sum_{{\varpi},{\sigma}}^{S,D}}(t,{\kappa},{\rho})$ for -1 ≤ D < S ≤ 1, this paper aims to determine sufficient conditions, distortion properties and radii of starlikeness and convexity for functions in the subclass $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.