• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.545-555
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• 2009

In this paper, we investigate a generalized family of complex-valued harmonic functions that are multivalent, sense-preserving, and are associated with k-uniformly harmonic functions in the unit disk. The results obtained here include a number of known and new results as their special cases.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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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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• v.49 no.4
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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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• v.28 no.1
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• pp.81-93
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• 2023

By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ A_p using this operator.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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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 $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.

• 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.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.387-400
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• 2023

The purpose of the present paper is to obtain some subordination and superordination preserving properties with the sandwich-type theorems for multivalent functions in the open unit disk associated with Srivastava-Attiya operator. Moreover, applications for integral operators are also considered.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.211-220
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• 2014

In the present investigation, by making use of the familiar concept of neighborhoods of analytic and multivalent functions, we prove several inclusion relations associated with the (n, ${\delta}$)-neighborhoods of certain subclasses of analytic functions of complex order, which are introduced here by means of the Al-Oboudi derivative. Several special cases of the main results are mentioned.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.21-32
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• 2012

In this paper a new subclass of multivalent functions with negative coefficients defined by Cho-Kwon-Srivastava operator is introduced. Coefficient estimate and inclusion relationships involving the neighborhoods of p-valently analytic functions are investigated for this class. Further subordination result and results on partial sums for this class are also found.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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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.