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Certain differential subordinations using a generalized Salagean operator and Ruscheweyh operator

Lupas A. A.

Journal of Mathematics and Applications

2010

Vol. 33

67-72

In the present paper we define a new operator using the generalized Salagean operator and Ruscheweyh operator. Denote by [formula/wzór] the Hadamard product of the generalized Salagean operator [formula/wzór] and Ruscheweyh operator R(n), given by [fomula/wzór] is the class of normalized analytic functions with A1 = A. We study some differential subordinations regarding the operator [formula/wzór].

A new class of analytic functions based on Ruscheweyh derivative

Sudharsan T. V., Thirumalaisamy R., Sivasubramanian S., Subramanian K. G.

Journal of Mathematics and Applications

2010

Vol. 33

103-115

In this paper we introduce a new class [formula/wzór] consisting of analytic functions with negative coeffcients and investigate various properties and characterization of the class. The results include coeffcient estimates, distortion theorem, closure theorems and integral operators for the class [formula/wzór]. Also radii of close-to-convexity, starlikeness and convexity are determined.

The convolution of functions and distributions

Fisher B., Zhenhai L., Nicholas J.

Demonstratio Mathematica

2000

Vol. 33, nr 4

835-841

The non-commutative convolution product f* g of two distributions f and g in D' is defined to be the limit of the sequence {(/frn) * g}, provided the limit exists, where {r-n} is a certain sequence of functions rn in 'D converging to 1.