• Title/Summary/Keyword: convex and starlike functions

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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.

NORMALIZED DINI FUNCTIONS CONNECTED WITH k-UNIFORMLY CONVEX AND k-STARLIKE FUNCTIONS

  • ECE, SADETTIN;EKER, SEVTAP SUMER;SEKER, BILAL
    • Journal of applied mathematics & informatics
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    • v.39 no.5_6
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    • pp.717-723
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    • 2021
  • The purpose of the present paper is to give sufficient conditions for normalized Dini function which is the special combination of the generalized Bessel function of first kind to be in the classes k-starlike functions and k-uniformly convex functions.

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.

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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Some Inclusion Properties of New Subclass of Starlike and Convex Functions associated with Hohlov Operator

  • Sokol, Janusz;Murugusundaramoorthy, Gangadharan;Kothandabani, Thilagavathi
    • Kyungpook Mathematical Journal
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    • v.56 no.2
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    • pp.597-610
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    • 2016
  • For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

CLASS-MAPPING PROPERTIES OF THE HOHLOV OPERATOR

  • Mishra, Akshaya K.;Panigrahi, Trailokya
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.51-65
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    • 2011
  • In the present paper sufficient conditions, in terms of hyper-geometric inequalities, are found so that the Hohlov operator preserves a certain subclass of close-to-convex functions (denoted by $R^{\tau}$ (A, B)) and transforms the classes consisting of k-uniformly convex functions, k-starlike functions and univalent starlike functions into $\cal{R}^{\tau}$ (A, B).

HARMONIC MEROMORPHIC STARLIKE FUNCTIONS

  • Jahangiri, Jay, M.
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.291-301
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    • 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.

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On a Class of Analytic Functions Related to the Starlike Functions

  • Gao, Chunyi;Zhou, Shiqiong
    • Kyungpook Mathematical Journal
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    • v.45 no.1
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    • pp.123-130
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    • 2005
  • In this paper we discuss a class of analytic functions related to the starlike functions in the unit disk. We prove that this class belongs to the class of close-to-convex functions, we obtain the sharp coefficient upper bounds and distortion theorem of this class, we also get the convexity radius of this class.

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