• Title, Summary, Keyword: Ruscheweyh derivative

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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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Some New Subclasses of Analytic Functions defined by Srivastava-Owa-Ruscheweyh Fractional Derivative Operator

  • Noor, Khalida Inayat;Murtaza, Rashid;Sokol, Janusz
    • Kyungpook Mathematical Journal
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    • v.57 no.1
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    • pp.109-124
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    • 2017
  • In this article the Srivastava-Owa-Ruscheweyh fractional derivative operator $\mathcal{L}^{\alpha}_{a,{\lambda}}$ is applied for defining and studying some new subclasses of analytic functions in the unit disk E. Inclusion results, radius problem and other results related to Bernardi integral operator are also discussed. Some applications related to conic domains are given.

UPPER BOUND ON THE THIRD HANKEL DETERMINANT FOR FUNCTIONS DEFINED BY RUSCHEWEYH DERIVATIVE OPERATOR

  • Yavuz, Tugba
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.437-444
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    • 2018
  • Let S denote the class of analytic and univalent functions in the open unit disk $D=\{z:{\mid}z{\mid}<1\}$ with the normalization conditions f(0) = 0 and f'(0) = 1. In the present article, an upper bound for third order Hankel determinant $H_3(1)$ is obtained for a certain subclass of univalent functions generated by Ruscheweyh derivative operator.

ON A CLASS OF ANALYTIC FUNCTIONS INVOLVING RUSCHEWEYH DERIVATIVES

  • Yang, Dinggong;Liu, Jinlin
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.123-131
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    • 2002
  • Let A(p, k) (p, k$\in$N) be the class of functions f(z) = $z^{p}$ + $a_{p+k}$ $z^{p+k}$+… analytic in the unit disk. We introduce a subclass H(p, k, λ, $\delta$, A, B) of A(p, k) by using the Ruscheweyh derivative. The object of the present paper is to show some properties of functions in the class H(p, k, λ, $\delta$, A, B). B).

On Sufficient Conditions for Certain Subclass of Analytic Functions Defined by Convolution

  • Sooriyakala, Paramasivam;Marikkannan, Natarajan
    • Kyungpook Mathematical Journal
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    • v.49 no.1
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    • pp.47-55
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    • 2009
  • In the present investigation sufficient conditions are found for certain subclass of normalized analytic functions defined by Hadamard product. Differential sandwich theorems are also obtained. As a special case of this we obtain results involving Ruscheweyh derivative, S$\u{a}$l$\u{a}$gean derivative, Carlson-shaffer operator, Dziok-Srivatsava linear operator, Multiplier transformation.

On a Class of Univalent Functions Defined by Ruscheweyh Derivatives

  • SHAMS, S.;KULKARNI, S.R.;JAHANGIRI, JAY M.
    • Kyungpook Mathematical Journal
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    • v.43 no.4
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    • pp.579-585
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    • 2003
  • A new class of univalent functions is defined by making use of the Ruscheweyh derivatives. We provide necessary and sufficient coefficient conditions, extreme points, integral representations, distortion bounds, and radius of starlikeness and convexity for this class.

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HIGHER ORDER CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH RUSCHEWEYH DERIVATIVE OPERATOR

  • NOOR, KHALIDA INAYAT;SHAH, SHUJAAT ALI
    • Journal of applied mathematics & informatics
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    • v.39 no.1_2
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    • pp.133-143
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    • 2021
  • The purpose of this paper is to introduce and study certain subclasses of analytic functions by using Ruscheweyh derivative operator. We discuss various of interesting properties such as, necessary condition, arc length problem and growth rate of coefficient of newly defined class. Also rate of growth of Hankel determinant will be estimated.

On Certain Novel Subclasses of Analytic and Univalent Functions

  • Irmak, Huseyin;Joshi, Santosh Bhaurao;Raina, Ravinder Krishen
    • Kyungpook Mathematical Journal
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    • v.46 no.4
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    • pp.543-552
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    • 2006
  • The purpose of the present paper is to introduce two novel subclasses $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$ and $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$. These results are then appropriately applied to derive similar geometrical properties for the other class $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.

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