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

Bednarz U.

Journal of Mathematics and Applications

2007

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.

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

Bednarz U., Kanas S.

Journal of Applied Analysis

2004

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.

Singular filters for the radon backprojection

Hungerbühler N.

Journal of Applied Analysis

1999

Vol. 5, nr 1

17-33

Numerous methods for the inversion of the Radon transformation which is the basis of computerized tomography are known: Fourier inversion, filtered backprojection or Kaczmarz's method. In the filtered backprojection method the choice of the filter function is crucial for the quality of the pictures. Here we deal with singular filter functions which have some advantages in comparison with conventional filters. An adapted method allows to handle the numerical problems caused by the singularities.