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

• Autorzy: Bednarz U.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

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

PL

funkcja jednostajnie wypukła; funkcja gwiaździsta; splot funkcji; splot Hadamarda; iloczyn Hadamarda; splot funkcji całkowy; przekształcenie całkowe; otoczenie funkcji

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2007
• Tom: Vol. 29
• Strony: 91--98
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Bednarz U.

• Deprtment of Mathematics Rzeszów University of Technology W. Pola 2, P.O. Box 85 35-959 Rzeszów, Poland,

Bibliografia

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