• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.327-333
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• 2015

In this paper, we introduce a class of p-valent meromorphic functions associated with linear operator and derive several interesting results of this class.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.513-522
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• 2021

In this current study, we aim to give some applications on fourth-order differential subordination for p-valent meromorphic functions in the region U^* = {z ∈ ℂ : 0 < |z| < 1} = U∖{0}, where U = {z ∈ ℂ : |z| < 1} , involving the linear operator 𝓛^*_pf. By making use of basic concepts in theory of the fourth-order, we find new outcomes.

• 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.

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.57-63
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• 2005

Let ∑(p)(p ∈ N) be the class of functions f(z) = z/sup -p/ + α/sub 1-p/ z/sup 1-p/ + α/sub 2-p/z/sup 2-p/ + ... analytic in 0 < ｜z｜ < 1 and let M(p, λ, μ)(0 < λ≤ 2 and 2λ(λ - 1) ≤ μ ≤ λ²) denote the class of functions f(z) ∈ ∑(p) which satisfy (equation omitted). The object of the present paper is to derive some properties of functions in the class M(p, λ, μ).

• East Asian mathematical journal
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• v.7 no.2
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• pp.157-164
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• 1992

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.971-977
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• 2017

For $p{\in}{\mathbb{N}}^{\ast}$ let ${\Sigma}_{p,0}$ denote the class of meromorphic functions of the form $g(z) ={\frac{1}{z^p}}+a_0+a_1z+{\cdots}$, $z{\in}U$. In the present paper we introduce a new subclass of the class ${\Sigma}_{p,0}$, using the subordination and the operator $J^n_{p,{\lambda}}$. This class will be denoted by $B^n_{p,{\lambda}}({\alpha},h)$ and we study some inclusion properties of this subclass.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.631-646
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• 2009

In the present investigation, we introduce new classes of p-valent meromorphic functions defined by Liu-Srivastava linear operator and the multiplier transform and study their properties by using certain first order differential subordination and superordination.