• Title, Summary, Keyword: starlike functions

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Radius of Starlikeness for Analytic Functions with Fixed Second Coefficient

  • Ali, Rosihan M.;Kumar, Virendra;Ravichandran, V.;Kumar, Shanmugam Sivaprasad
    • Kyungpook Mathematical Journal
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    • v.57 no.3
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    • pp.473-492
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    • 2017
  • Sharp radius constants for certain classes of normalized analytic functions with fixed second coefficient, to be in the classes of starlike functions of positive order, parabolic starlike functions, and Sokół-Stankiewicz starlike functions are obtained. Our results extend several earlier works.

Certain Subclasses of k-Uniformly Starlike and Convex Functions of Order α and Type β with Varying Argument Coefficients

  • AOUF, MOHAMED KAMAL;MAGESH, NANJUNDAN;YAMINI, JAGADESAN
    • Kyungpook Mathematical Journal
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    • v.55 no.2
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    • pp.383-394
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    • 2015
  • In this paper, we define two new subclass of k-uniformly starlike and convex functions of order ${\alpha}$ type ${\beta}$ with varying argument of coefficients. Further, we obtain coefficient estimates, extreme points, growth and distortion bounds, radii of starlikeness, convexity and results on modified Hadamard products.

A Class of Starlike Functions Defined by the Dziok-Srivastava Operator

  • Silverman, Herb;Murugusundaramoorhty, Gangadharan;Vijaya, Kaliappan
    • Kyungpook Mathematical Journal
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    • v.49 no.1
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    • pp.95-106
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    • 2009
  • A comprehensive class of starlike univalent functions defined by Dziok-Srivastava operator is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Further distortion bounds, extreme points and results on partial sums are investigated.

THIRD HANKEL DETERMINANTS FOR STARLIKE AND CONVEX FUNCTIONS OF ORDER ALPHA

  • Orhan, Halit;Zaprawa, Pawel
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.165-173
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    • 2018
  • In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^*({\alpha})$ of starlike functions of order ${\alpha}$ and $\mathcal{K}({\alpha}$) of convex functions of order ${\alpha}$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.

First Order Differential Subordinations for Carathéodory Functions

  • Gandhi, Shweta;Kumar, Sushil;Ravichandran, V.
    • Kyungpook Mathematical Journal
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    • v.58 no.2
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    • pp.257-270
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    • 2018
  • The well-known theory of differential subordination developed by Miller and Mocanu is applied to obtain several inclusions between $Carath{\acute{e}}odory$ functions and starlike functions. These inclusions provide sufficient conditions for normalized analytic functions to belong to certain class of Ma-Minda starlike functions.

SOME MAJORIZATION PROBLEMS ASSOCIATED WITH p-VALENTLY STARLIKE AND CONVEX FUNCTIONS OF COMPLEX ORDER

  • Altintas, Osman;Srivastava, H.M.
    • East Asian mathematical journal
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    • v.17 no.2
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    • pp.175-183
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    • 2001
  • The main object of this paper is to investigate several majorization problems involving two subclasses $S_{p,q}(\gamma)$ and $C_{p,q}(\gamma)$ of p-valently starlike and p-valently convex functions of complex order ${\gamma}{\neq}0$ in the open unit disk $\mathbb{u}$. Relevant connections of the results presented here with those given by earlier workers on the subject are also indicated.

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ON SUFFICIENT CONDITIONS FOR CARATHÉODORY FUNCTIONS WITH THE FIXED SECOND COEFFICIENT

  • Kwon, Oh Sang
    • Honam Mathematical Journal
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    • v.41 no.2
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    • pp.227-242
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    • 2019
  • In the present paper, we derive several sufficient conditions for $Carath{\acute{e}}odory$ functions in the open unit disk ${\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$ under the constraint that the second coefficient of the function is preassigned. And, we obtain some sufficient conditions for strongly starlike functions in ${\mathbb{D}}$.