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On certain subclasses of meromorphically multivalent functions associated with a certain linear operator

100%

Aouf M. K. , Murugusundaramoorthy G.

Journal of Mathematics and Applications

2007

tom Vol. 29

33-52

In this paper we introduce and study two subclasses (Rn,p(α, A, B)) and Sn,p(α, A, B)) of meromorphic p-valent functions of order α (0 ≤ α < p) defined by certain linear operator. We investigate the various important properties and characteristics of these subclasses. Some properties of neighborhoods of functions in these subclasses are investigated. Also we derive many interesting results for the Hadamard products of functions belonging to the class Sn,p(α, A, B).

Stability of the integral transformation of k-uniformly convex and k-starlike functions

80%

Bednarz U.

Journal of Mathematics and Applications

2007

tom Vol. 29

91-98

For a constant k ϵ [0, ∞) a normalized function f, analytic in the unit disk, is said to be k-uniformly convex if Re (1+z f" (z)/f'(z)) > k|zf"(z)/f'(z)| at any point in the unit disk. The class of k-uniformly convex functions is denoted k-UCV (cf. [8]). The function g is said to be k-starlike if g(z) = zf'(z) and f ϵ k-UCV. For analytic function f, where f(z) = z + a2z² + źźź the integral transformation is defined as follows: [wzór]. Generalized neighbourhood is defined as: [wzór]. In this note a problem of stability of the integral transformation of k-uniformly convex and k-starlike functions for TNδ neighbourhoods is investigated.

On T-neighborhoods of analytic functions

80%

Bednarz U. , Sokół J.

Journal of Mathematics and Applications

2010

tom Vol. 32

25-32

Stability of the integral convolution of k-uniformly convex and k-starlike functions

80%

Bednarz U. , Kanas S.

Journal of Applied Analysis

2004

tom Vol. 10, nr 1

105-115

For a constant k ∈ [0, ∞) a normalized function f, analytic in the unit disk, is said to be k-uniformly convex if Re(1 + zf"(z)/f'(z)) > k|zf"(z)/f'(z)| at any point in the unit disk. The class of k-uniformly convex functions is denoted k-UCV (cf. [4]). The function g is said to be k-starlike if g(z) = zf'(z) and f ∈ k-UCV. For analytic functions f, g, where f(z) = z + a2z² + • • • and g(z) = z + b2z² + • • •, the integral convolution is defined as follows: [wzór] In this note a problem of stability of the integral convolution of k-uniformly convex and k-starlike functions is investigated.