• 대한수학회보
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• 제40권4호
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• pp.553-564
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• 2003

We give sufficient coefficient conditions for starlikeness of a class of complex-valued multivalent meromorphic harmonic and orientation preserving functions in outside of the unit disc. These coefficient conditions are also shown to be necessary if the coefficients of the analytic part of the harmonic functions are positive and the coefficients of the co-analytic part of the harmonic functions are negative. We then determine the extreme points, distortion bounds, convolution and convex combination conditions for these functions.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.713-723
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• 2009

The purpose of the present paper is to introduce a new subclass of meromorphic multivalent functions defined by using a linear operator associated with the generalized hypergeometric function. Some properties of this class are established here by using the principle of differential subordination and convolution in geometric function theory.

• 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 $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.

• 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.

• 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.