• Title, Summary, Keyword: starlike

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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.

ON THE COEFFICIENTS OF GAMMA-STARLIKE FUNCTIONS

  • Thomas, Derek K.
    • Journal of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.175-184
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    • 2018
  • We give several sharp estimates for some initial coefficients problems for the so-called gamma starlike functions f, analytic and univalent in the unit disk ${\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$, and normalized so that f(0) = 0 = f'(0)-1, and satisfying Re $\left[\left(1+{\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}}\right)^{\gamma}\left({\frac{zf^{\prime}(z)}{f(z)}}\right)^{1-{\gamma}}\right]$ > 0.

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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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).