• Title/Summary/Keyword: Starlike functions

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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).

HANKEL DETERMINANTS FOR STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRICAL POINTS

  • Nak Eun Cho;Young Jae Sim;Derek K. Thomas
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.2
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    • pp.389-404
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    • 2023
  • We prove sharp bounds for Hankel determinants for starlike functions f with respect to symmetrical points, i.e., f given by $f(z)=z+{\sum{_{n=2}^{\infty}}}\,{\alpha}_nz^n$ for z ∈ 𝔻 satisfying $$Re{\frac{zf^{\prime}(z)}{f(z)-f(-z)}}>0,\;z{\in}{\mathbb{D}}$$. We also give sharp upper and lower bounds when the coefficients of f are real.

PARTIAL SUMS AND INCLUSION RELATIONS FOR STARLIKE FUNCTIONS ASSOCIATED WITH AN EVOLUTE OF A NEPHROID CURVE

  • Gurpreet Kaur ;Sumit Nagpal
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.6
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    • pp.1477-1496
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    • 2023
  • A class of normalized univalent functions f defined in an open unit disk of the complex plane is introduced and studied such that the values of the quantity zf'(z)/f(z) lies inside the evolute of a nephroid curve. The inclusion relations of the newly defined class with other subclasses of starlike functions and radius problems concerning the second partial sums are investigated. All the obtained results are sharp.

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.

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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Partial Sums of Starlike Harmonic Univalent Functions

  • Porwal, Saurabh;Dixit, Kaushal Kishore
    • Kyungpook Mathematical Journal
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    • v.50 no.3
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    • pp.433-445
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    • 2010
  • Although, interesting properties on the partial sums of analytic univalent functions have been investigated extensively by several researchers, yet analogous results on partial sums of harmonic univalent functions have not been so far explored. The main purpose of the present paper is to establish some new and interesting results on the ratio of starlike harmonic univalent function to its sequences of partial sums.