• 제목/요약/키워드: Starlike functions

검색결과 177건 처리시간 0.019초

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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    • 제57권3호
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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.

SUFFICIENT CONDITIONS FOR STARLIKENESS OF RECIPROCAL ORDER

  • Saravanarasu Madhumitha;Vaithiyanathan Ravichandran
    • Korean Journal of Mathematics
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    • 제31권3호
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    • pp.243-258
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    • 2023
  • A normalized analytic function f defined on the unit disk 𝔻 is starlike of reciprocal order α, 0 ≤ α < 1, if Re(f(z)/(zf'(z))) > α for all z ∈ 𝔻. Such functions are starlike and therefore univalent in 𝔻. Using the well-known Miller-Mocanu differential subordination theory, sufficient conditions involving differential inclusions are obtained for a normalized analytic function to be starlike of reciprocal order α. Furthermore, a few conditions are derived for a function f to belong to a subclass of reciprocal starlike functions, satisfying |f(z)/(zf'(z)) - 1| < 1 - α.

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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    • 제55권2호
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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.

On Coefficients of a Certain Subclass of Starlike and Bi-starlike Functions

  • Mahzoon, Hesam;Sokol, Janusz
    • Kyungpook Mathematical Journal
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    • 제61권3호
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    • pp.513-522
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    • 2021
  • In this paper we investigate a subclass 𝓜(α) of the class of starlike functions in the unit disk |z| < 1. 𝓜(α), π/2 ≤ α < π, is the set of all analytic functions f in the unit disk |z| < 1 with the normalization f(0) = f'(0) - 1 = 0 that satisfy the condition $$1+\frac{{\alpha}-{\pi}}{2\;sin\;{\alpha}}. The class 𝓜(α) was introduced by Kargar et al. [Complex Anal. Oper. Theory 11: 1639-1649, 2017]. In this paper some basic geometric properties of the class 𝓜(α) are investigated. Among others things, coefficients estimates and bound are given for the Fekete-Szegö functional associated with the k-th root transform [f(zk)]1/k. Also a certain subclass of bi-starlike functions is introduced and the bounds for the initial coefficients are obtained.

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

  • Silverman, Herb;Murugusundaramoorhty, Gangadharan;Vijaya, Kaliappan
    • Kyungpook Mathematical Journal
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    • 제49권1호
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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.

THE THIRD HERMITIAN-TOEPLITZ AND HANKEL DETERMINANTS FOR PARABOLIC STARLIKE FUNCTIONS

  • Rosihan M. Ali;Sushil Kumar;Vaithiyanathan Ravichandran
    • 대한수학회보
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    • 제60권2호
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    • pp.281-291
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    • 2023
  • A normalized analytic function f is parabolic starlike if w(z) := zf' (z)/f(z) maps the unit disk into the parabolic region {w : Re w > |w - 1|}. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

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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    • 제39권5_6호
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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
    • 대한수학회보
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    • 제55권1호
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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.