Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 5 (2010), 35 -- 47


Waggas Galib Atshan and S. R. Kulkarni

Abstract. For certain univalent function f, we study a class of functions f as defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator, satisfying

Re { (zJ1λ, μ f(z))')/((1 - γ) J1λ, μ f(z) + γ z2(J1λ, μ f(z))" )} > β.
A necessary and sufficient condition for a function to be in the class Aγλ, μ, ν(n, β) is obtained. In addition, our paper includes distortion theorem, radii of starlikeness, convexity and close-to-convexity, extreme points. Also, we get some results in this paper.

2000 Mathematics Subject Classification: 30C45.
Keywords: Distortion theorem; Radii of starlikeness; Extreme points.

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Waggas Galib Atshan S. R. Kulkarni
Department of Mathematics, Department of Mathematics,
College of Computer Science and Mathematics, Fergusson College, Pune - 411004,
University of AL-Qadisiya, Diwaniya, Iraq. India.
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