on his 65th Birth Anniversary This note investigates coefficient estimates and subordination properties for certain classes of normalized functions (which are essentially defined by means of a Hadamard product of two analytic functions). We exhibit several interesting consequences of our main results, and in the process, we are also led to the corrected forms of the results given by Owa and Nis...

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...

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.

In this paper, we introduce two subclasses Ωp(α) and Λ ∗ p(α) of meromorphic pvalent functions in the punctured diskD = {z : 0 < |z| < 1}. Coefficient inequalities, distortion theorems, the radii of starlikeness and convexity, closure theorems and Hadamard product ( or convolution) of functions belonging to these classes are obtained.

In the present paper, we investigate several inclusion relationships and other interesting properties of certain subclasses of meromorphically multivalent functions which are defined here by means of a linear operator involving the generalized hypergeometric function. Some interesting applications on Hadamard product concerning this and other classes of integral operators are also considered.

Generalizing [BrFa] we prove the existence of a bilipschitz embedded manifold of pinched negative curvature and dimension m1 +m2 −1 in the product X := Xm1 1 ×X m2 2 of two Hadamard manifolds Xmi i of dimension mi with pinched negative curvature. Combining this result with [BuySch] we prove the additivity of the hyperbolic rank for products of manifolds with pinched negative curvature.

In this paper we consider the modified Hadamard product or convolution of analytic functions with negative coefficients, combined with an Sǎlǎgean integral operator. We discuss when it is a given class. Following idea of U. Bednarz and J. Sokól we shall determine the order of convolution consistence for certain analytic functions with negative coefficients. AMS Subject Classification: 30C45, 30C50

We introduce a class Σ∗λ,p,α of meromorphic p-valent functions with negative coefficients. The main object of this paper is to investigate various important properties and characteristics of this class. Further many interesting results for the Hadamard product of functions belonging to the class Σ∗λ,p,α is obtained. 2000 Mathematics Subject Classification: 30C45.

A new subclass R(u), 0 < u < I, of the class St(I/2) the class of starlike functions of order I/2 is introduced and it is shown that R(u) is closed with respect to the Hadamard product of analytic functions. Some sufficient conditions for the normalized regular functions to be univalent in the unit disk E are given.

The main purpose of this paper is to derive some quasi-Hadamard product properties for certain classes of analytic functions which are defined by means of the Salagean operator. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.