T. N. Shanmugam1 and M. P. Jeyaraman2 1 Department of Mathematics, College of Engineering, Anna University, Chennai 600025, India 2 Department of Mathematics, Easwari Engineering College, Chennai 600089, India Correspondence should be addressed to M. P. Jeyaraman, jeyaraman [email protected] Received 27 July 2009; Accepted 8 October 2009 Recommended by Narendra Kumar Govil We apply the general the...

Abstract In the present investigation, we introduce and study interesting properties of a new unified class of pre-starlike functions with negative coefficients in the open unit disk ∆. These properties include growth and distortion, radii of convexity, radii of starlikeness and radii of close to convexity. 2000 Mathematics Subject Classification: 30C45.

For analytic functions f (z) = z p +a p+1 z p+1 +··· in the open unit disk U and a polynomial Q(z) of degree n > 0, the function F(z) = f (z)[Q(z)] β/n is introduced. The object of the present paper is to determine the radius of p-valently strongly starlikeness of order γ for F(z).

In this paper, we introduce a new class of functions which are analytic and univalent with negative coefficients defined by using a certain fractional calculus and fractional calculus integral operators. Characterization property,the results on modified Hadamard product and integrals transforms are discussed. Further, distortion theorem and radii of starlikeness and convexity are also determine...

Two classes ̄n(μ,α,λ) and ̄n(μ,α,λ) of analytic functions which are not Bazilevǐc type in the open unit disk U are introduced. The object of the present paper is to consider the starlikeness of functions belonging to the classes ̄n(μ,α,λ) and ̄n(μ,α,λ). 2000 Mathematics Subject Classification. 30C45.

Abstract. In this paper, we introduce a new class of functions which are analytic and univalent with negative coefficients defined by using certain fractional operators descibed in the Caputo sense. Characterization property, the results on modified Hadamard product and integral transforms are discussed. Further, distortion theorem and radii of starlikeness and convexity are also determined here.