Some applications of generalized Ruscheweyh derivatives involving a general fractional derivative operator to a class of analytic functions with negative coefficients I
Journal Title: Surveys in Mathematics and its Applications - Year 2010, Vol 5, Issue 0
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 <CENTER>Re { (zJ<SUB>1</SUB><SUP>λ, μ</SUP> f(z))<SUP>'</SUP>)/((1 -γ) J<SUB>1</SUB><SUP>λ, μ</SUP> f(z) + γ z<SUP>2</SUP>(J<SUB>1</SUB><SUP>λ, μ</SUP> f(z))<SUP>"</SUP> )} > β.</CENTER> A necessary and sufficient condition for a function to be in the class A<SUB>γ</SUB><SUP>λ, μ, ν</SUP>(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.
Authors and Affiliations
Waggas Galib Atshan, S. Kulkarni
Keywords
Related Articles
- EP ID EP139573
- DOI -
- Views 73
- Downloads 0
Magnetic field and thermal radiation effects on steady hydromagnetic Couette flow through a porous channel
This paper investigates effects of thermal radiation and magnetic field on hydromagnetic Couette flow of a highly viscous fluid with temperature-dependent viscosity and thermal conductivity at constant pressure through a...
Considerations on some algebraic properties of Feynman integrals
Some algebraic properties of integralsover configuration spaces are investigated in order to better understandquantization and the Connes-Kreimer algebraic approach to renormalization. <BR>In order to isolate the m...
Function valued metric spaces
In this paper we introduce the notion of an &#8497;-metric, as a function valued distance mapping, on a set X and we investigate the theory of &#8497;-metrics paces. We show that every metric space may be viewed...
New result of existence of periodic solution for a Hopfield neural networks with neutral time-varying delays
In this paper, a Hopfield neural network with neutral time-varying delays is investigated by using the continuation theorem of Mawhin's coincidence degree theory and some analysis technique. Without assuming the continuo...
On a recurrence relation of generalized Mittag-Leffler function
The principal aim of this paper is to investigate a recurrence relation and an integral representation of generalized Mittag-Leffler function E<SUB>α ,β </SUB><SUP>γ ,q</SUP> (z). In the end sever...