On some convolution theorems

• Autorzy: Piejko K.
• Języki publikacji: EN

Abstrakty

EN

Let ℌ be the class of functions regular in the unit disc. For two functions ƒ(z) = [formula], g (z) = [formula] of the class ℌ and for all complex m we define the convolution (ƒ★_m g) (z) [formula]. For given complex numbers a, A, B; aB ≠ A, |B| ≤ 1 we define P_a (A, B) := [formula]. The object of this paper is to give the solution of the problem of finding all m ϵ C, for which convolution ƒ★_m g belongs to the P_ab (X. Y) if ƒ ϵ P_a (A, B) and g ϵ P_b (C, D).

Słowa kluczowe

EN

convolution; subordination; circular domains

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2002
• Tom: [Z] 42(1)
• Strony: 103--112
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Piejko K.

• Department of Mathematics, Technical University of Rzeszów, ul. W. Pola 2, 35-959 Rzeszów, Polska,

Bibliografia

• [L] R. R. London, A convolution theorem for functions mapping the unit disc into half planes, Math. Japonica 43 No. l (1996), 23-29.
• [NN ] Z. Nehari and E. Netanyahu, On the coefficients of meromorphic sufficient functions, Proc. Amer. Math. Soc. 8 (1957), 15-23.
• [RS] S. Ruscheweyh and J. Stankiewicz, Subordination under convex univalent functions, Bull. Pol. Acad. Sci. Math. 33 (1985), 499-502.
• [SS] J. Stankiewicz and Z. Stankiewicz, Convolution of some classes of function, Folia Sci. Univ. Techn. Resov. 48 (1988), 93-101.