• Title/Summary/Keyword: meromorphic starlike

Search Result 10, Processing Time 0.017 seconds

HARMONIC MEROMORPHIC STARLIKE FUNCTIONS

  • Jahangiri, Jay, M.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.37 no.2
    • /
    • pp.291-301
    • /
    • 2000
  • We give sufficient coefficient conditions for a class of meromorphic univalent harmonic functions that are starlike of some order. Furthermore, it is shown that these conditions are also necessary when the coefficients of the analytic part of the function are positive and the coefficients of the co-analytic part of the function are negative. Extreme points, convolution and convex combination conditions for these classes are also determined. Fianlly, comparable results are given for the convex analogue.

  • PDF

Argument Estimates Of Certain Meromorphic Functions

  • Cho, Nak-Eun
    • Communications of the Korean Mathematical Society
    • /
    • v.15 no.2
    • /
    • pp.263-274
    • /
    • 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.

  • PDF

PARTIAL SUMS AND NEIGHBORHOODS OF JANOWSKI-TYPE SUBCLASSES OF MEROMORPHIC FUNCTIONS

  • Abdullah Alatawi;Maslina Darus
    • Korean Journal of Mathematics
    • /
    • v.31 no.3
    • /
    • pp.259-267
    • /
    • 2023
  • The paper presents the introduction of a novel linear derivative operator for meromorphic functions that are linked with q-calculus. Using the linear derivative operator, a new category of meromorphic functions is generated in the paper. We obtain sufficient conditions and show some properties of functions belonging to these subclasses. The partial sums of its sequence and the q-neighborhoods problem are solved.

STARLIKENESS OF MULTIVALENT MEROMORPHIC HARMONIC FUNCTIONS

  • Murugusundaramoorthy, G.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.40 no.4
    • /
    • pp.553-564
    • /
    • 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.

Convolution Properties of Certain Class of Multivalent Meromorphic Functions

  • Vijaywargiya, Pramila
    • Kyungpook Mathematical Journal
    • /
    • v.49 no.4
    • /
    • pp.713-723
    • /
    • 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.

A CRITERION FOR BOUNDED FUNCTIONS

  • Nunokawa, Mamoru;Owa, Shigeyoshi;Sokol, Janusz
    • Bulletin of the Korean Mathematical Society
    • /
    • v.53 no.1
    • /
    • pp.215-225
    • /
    • 2016
  • We consider a sufficient condition for w(z), analytic in ${\mid}z{\mid}$ < 1, to be bounded in ${\mid}z{\mid}$ < 1, where $w(0)=w^{\prime}(0)=0$. We apply it to the meromorphic starlike functions. Also, a certain Briot-Bouquet differential subordination is considered. Moreover, we prove that if $p(z)+zp^{\prime}(z){\phi}(p(z)){\prec}h(z)$, then $p(z){\prec}h(z)$, where $h(z)=[(1+z)(1-z)]^{\alpha}$, under some additional assumptions on ${\phi}(z)$.

SOME EXTENSION RESULTS CONCERNING ANALYTIC AND MEROMORPHIC MULTIVALENT FUNCTIONS

  • Ebadian, Ali;Masih, Vali Soltani;Najafzadeh, Shahram
    • Bulletin of the Korean Mathematical Society
    • /
    • v.56 no.4
    • /
    • pp.911-927
    • /
    • 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.

ON A CLASS OF MEROMORPHICALLY P-VALENT STARLIKE FUNCTIONS

  • Xu NENG;YANG DINGGONG
    • The Pure and Applied Mathematics
    • /
    • v.12 no.1
    • /
    • pp.57-63
    • /
    • 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).

  • PDF

On the Fekete-Szegö Problem for a Certain Class of Meromorphic Functions Using q-Derivative Operator

  • Aouf, Mohamed Kamal;Orhan, Halit
    • Kyungpook Mathematical Journal
    • /
    • v.58 no.2
    • /
    • pp.307-318
    • /
    • 2018
  • In this paper, we obtain $Fekete-Szeg{\ddot{o}}$ inequalities for certain class of meromorphic functions f(z) for which $-{\frac{(1-{\frac{{\alpha}}{q}})qzD_qf(z)+{\alpha}qzD_q[zD_qf(z)]}{(1-{\frac{{\alpha}}{q}})f(z)+{\alpha}zD_qf(z)}{\prec}{\varphi}(z)$(${\alpha}{\in}{\mathbb{C}}{\backslash}(0,1]$, 0 < q < 1). Sharp bounds for the $Fekete-Szeg{\ddot{o}}$ functional ${\mid}{\alpha}_1-{\mu}{\alpha}^2_0{\mid}$ are obtained.

NEW SUBCLASS OF MEROMORPHIC MULTIVALENT FUNCTIONS ASSOCIATED WITH HYPERGEOMETRIC FUNCTION

  • Khadr, Mohamed A.;Ali, Ahmed M.;Ghanim, F.
    • Nonlinear Functional Analysis and Applications
    • /
    • v.26 no.3
    • /
    • pp.553-563
    • /
    • 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 $L^{t,{\rho}}_{{\varpi},{\sigma}}f(\zeta)$.