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

• Autorzy: Bednarz U. , Kanas S.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

k-uniformly convex functions; k-starlike functions; Hadamard product (or convolution); integral convolution; integral transformation; neighbourhoods of functions; stability of convolution

PL

k-jednostajne funkcje wypukłe; k-funkcje gwieździste; iloczyn Hadamarda; splot całkowy; całkowe przekształcenie; otoczenie funkcji; stabilność splotu

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2004
• Tom: Vol. 10, nr 1
• Strony: 105--115
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Bednarz U.

• Department of Mathematics Technical University of Rzeszów W. Pola 2 Pl-35-959 Rzeszów, Poland

autor

Kanas S.

• Department of Mathematics Technical University of Rzeszów W. Pola 2 Pl-35-959 Rzeszów, Poland

Bibliografia

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