• 제목/요약/키워드: Salagean operator

검색결과 6건 처리시간 0.02초

NEIGHBORHOODS OF CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • Darwish, Hanan E.;Aouf, Mohamed K.
    • 대한수학회보
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    • 제48권4호
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    • pp.689-695
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    • 2011
  • The main object of this paper is to prove several inclusion relations associated with (j, ${\delta}$)-neighborhoods of various subclasses defined by Salagean operator by making use of the familiar concept of neighborhoods of analytic functions. Special cases of some of these inclusion relations are shown to yield known results.

ON A NEW CLASS OF SALAGEAN-TYPE HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH SUBORDINATION

  • Altinkaya, Sahsene;Cakmak, Serkan;Yalcin, Sibel
    • 호남수학학술지
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    • 제40권3호
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    • pp.433-446
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    • 2018
  • In this present investigation, we introduce a new class of harmonic univalent functions of the form $f=h+{\bar{g}}$ in the open unit disk ${\Delta}$. We get basic properties, like, necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for these classes of functions.

On the Fekete-Szegö Problem for Starlike Functions of Complex Order

  • Darwish, Hanan;Lashin, Abdel-Moniem;Al Saeedi, Bashar
    • Kyungpook Mathematical Journal
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    • 제60권3호
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    • pp.477-484
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    • 2020
  • For a non-zero complex number b and for m and n in 𝒩0 = {0, 1, 2, …} let Ψn,m(b) denote the class of normalized univalent functions f satisfying the condition ${\Re}\;\[1+{\frac{1}{b}}\(\frac{D^{n+m}f(z)}{D^nf(z)}-1\)\]\;>\;0$ in the unit disk U, where Dn f(z) denotes the Salagean operator of f. Sharp bounds for the Fekete-Szegö functional |a3 - 𝜇a22| are obtained.

On Generalized Integral Operator Based on Salagean Operator

  • Al-Kharsani, Huda Abdullah
    • Kyungpook Mathematical Journal
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    • 제48권3호
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    • pp.359-366
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    • 2008
  • Let A(p) be the class of functions $f\;:\;z^p\;+\;\sum\limits_{j=1}^{\infty}a_jz^{p+j}$ analytic in the open unit disc E. Let, for any integer n > -p, $f_{n+p-1}(z)\;=\;z^p+\sum\limits_{j=1}^{\infty}(p+j)^{n+p-1}z^{p+j}$. We define $f_{n+p-1}^{(-1)}(z)$ by using convolution * as $f_{n+p-1}\;*\;f_{n+p-1}^{-1}=\frac{z^p}{(1-z)^{n+p}$. A function p, analytic in E with p(0) = 1, is in the class $P_k(\rho)$ if ${\int}_0^{2\pi}\|\frac{Re\;p(z)-\rho}{p-\rho}\|\;d\theta\;\leq\;k{\pi}$, where $z=re^{i\theta}$, $k\;\geq\;2$ and $0\;{\leq}\;\rho\;{\leq}\;p$. We use the class $P_k(\rho)$ to introduce a new class of multivalent analytic functions and define an integral operator $L_{n+p-1}(f)\;\;=\;f_{n+p-1}^{-1}\;*\;f$ for f(z) belonging to this class. We derive some interesting properties of this generalized integral operator which include inclusion results and radius problems.

ON A SUBCLASS OF CERTAIN STARLIKE FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • Kamali, Muhammet;Orhan, Halit
    • 대한수학회보
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    • 제41권1호
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    • pp.53-71
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    • 2004
  • A certain subclass $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$ of starlike functions in the unit disk is introduced. The object of the present paper is to derive several interesting properties of functions belonging to the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$. Coefficient inequalities, distortion theorems and closure theorems of functions belonging to the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$ are determined. Also we obtain radii of convexity for the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$. Furthermore, integral operators and modified Hadamard products of several functions belonging to the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$ are studied here.