• Title, Summary, Keyword: starlikeness

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A STARLIKENESS CONDITION ASSOCIATED WITH THE RUSCHEWEYH DERIVATIVE

  • Li, Jian-Lin;Srivastava, H.M.
    • East Asian mathematical journal
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    • v.18 no.1
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    • pp.1-13
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    • 2002
  • Some Miller-Mocanu type arguments are used here in order to establish a general starlikeness condition involving the familiar Ruscheweyh derivative. Relevant connections with the various known starlikeness conditions are also indicated. This paper concludes with several remarks and observations in regard especially to the nonsharpness of the main starlike condition presented here.

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Radii of Starlikeness and Convexity for Analytic Functions with Fixed Second Coefficient Satisfying Certain Coefficient Inequalities

  • MENDIRATTA, RAJNI;NAGPAL, SUMIT;RAVICHANDRAN, V.
    • Kyungpook Mathematical Journal
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    • v.55 no.2
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    • pp.395-410
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    • 2015
  • For functions $f(z)=z+a_2z^2+a_3z^3+{\cdots}$ with ${\mid}a_2{\mid}=2b$, $b{\geq}0$, sharp radii of starlikeness of order ${\alpha}(0{\leq}{\alpha}<1)$, convexity of order ${\alpha}(0{\leq}{\alpha}<1)$, parabolic starlikeness and uniform convexity are derived when ${\mid}a_n{\mid}{\leq}M/n^2$ or ${\mid}a_n{\mid}{\leq}Mn^2$ (M>0). Radii constants in other instances are also obtained.

PRODUCT AND CONVOLUTION OF CERTAIN UNIVALENT FUNCTIONS

  • Jain, Naveen Kumar;Ravichandran, V.
    • Honam Mathematical Journal
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    • v.38 no.4
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    • pp.701-724
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    • 2016
  • For $f_i$ belonging to various subclasses of univalent functions, we investigate the product given by $h(z)=z{\prod_{i=1}^{n}}(f_i(z)/z)^{{\gamma}_i}$.The largest radius ${\rho}$ is determined such that $h({\rho}z)/{\rho}$ is starlike of order ${\beta}$, $0{\leq}{\beta}$ < 1 or to belong to other subclasses of univalent functions. We also determine the sharp radius of starlikeness of order ${\beta}$and other radius for the convolution f*g of two starlike functions f, g.

STARLIKENESS OF MULTIVALENT MEROMORPHIC HARMONIC FUNCTIONS

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