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1

On an application of certain sufficient condition for starlikeness

Sokół J.

Journal of Mathematics and Applications

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2008

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Vol. 30

131-135

EN

In this paper we consider a sufficient condition for furiction to be a-starlike function, when α ∈ [0, 1/2]. We use it for certain subclass of strongly starlike functions defined by a geometric condition. We take advantage of the techniąues of differential subordinations.

2

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

Bednarz U.

Journal of Mathematics and Applications

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2007

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Vol. 29

91-98

EN

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.

3

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

Bednarz U., Kanas S.

Journal of Applied Analysis

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2004

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Vol. 10, nr 1

105-115

EN

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.

4

Generalized neighbourhoods and stability of convolution for the class of k-uniformly convex and k-starlike functions

Bednarz U., Kanas S.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

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1999

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z. 23 [175]

29-38

EN

Let k-UCV denote the class of k-uniformly convex functions and let k-ST be the related class of k-starlike functions. For [..] > 0 and nonnegative sequence {tn] we define generalized neighbourhood [...].

5

Differential subordinationfor domains bounded by hyperbolas

Kanas S., Lecko A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

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1999

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z. 23 [175]

61-70

EN

Let the function pa,b,s-so with a, b real, nonnegative numbers and s, so is an element of R, be a conform al mapping of the unit disk onto a hyperbolic domain. We establish the conditions udner which the differential subordination of the type p(z) +[...]zp'(z) -< pa,b,s-so(^) yields p -< pa,b,s- so(z) yields p [...] pa,b,s in U. Some applications of obtained results are given.