caa a22 4500 378915363 CHVBK 20180305123551.0 cr unu---uuuuu 161128e200406 xx s 000 0 eng 10.1515/JAA.2004.105 doi (NATIONALLICENCE)gruyter-10.1515/JAA.2004.105 Stability of the Integral Convolution of k-Uniformly Convex and k-Starlike Functions [Elektronische Daten] [U. Bednarz, S. Kanas] 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. [Kanas, Wiśniowska, J. Comput. Appl. Math. 105: 327-336, 1999]). 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 + a 2 z 2 + ⋯ and g(z) = z + b 2 z 2 + ⋯, the integral convolution is defined as follows: In this note a problem of stability of the integral convolution of k-uniformly convex and k-starlike functions is investigated. © Heldermann Verlag k-uniformly convex functions nationallicence k-starlike functions nationallicence Hadamard product (or convolution) nationallicence integral convolution nationallicence integral transformation nationallicence neighbourhoods of functions nationallicence stability of convolution nationallicence Bednarz U. Department of Mathematics, Technical University of Rzeszów, W. Pola 2, PL-35-959 Rzeszów, Poland. email: ubednarz@prz.edu.pl aut Kanas S. Department of Mathematics, Technical University of Rzeszów, W. Pola 2, PL-35-959 Rzeszów, Poland. email: skanas@prz.edu.pl aut Journal of Applied Analysis Walter de Gruyter GmbH & Co. KG 10/1(2004-06), 105-115 1425-6908 10:1<105 2004 10 JAA https://doi.org/10.1515/JAA.2004.105 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/JAA.2004.105 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bednarz U. Department of Mathematics, Technical University of Rzeszów, W. Pola 2, PL-35-959 Rzeszów, Poland. email: ubednarz@prz.edu.pl aut NATIONALLICENCE 700 1- Kanas S. Department of Mathematics, Technical University of Rzeszów, W. Pola 2, PL-35-959 Rzeszów, Poland. email: skanas@prz.edu.pl aut NATIONALLICENCE 773 0- Journal of Applied Analysis Walter de Gruyter GmbH & Co. KG 10/1(2004-06), 105-115 1425-6908 10:1<105 2004 10 JAA CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter