AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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STUDIA MATHEMATICA - Ediţia nr.2 din 2012 | |||||||
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SOME PROPERTIES ON GENERALIZED CLOSE-TO-STAR FUNCTIONS. Autori: . |
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Rezumat: Let f(z) = a1z+a1z2 +... , a1≠ 0, be regular in |z| < 1 and have there no zeros except at the origin. Reade ([3]) and the Sakaguchi ([2]) showed that a necessary and sufficient condition for f(z) to be a member of the class C(k) is that f(z) has a representation of the form f(z) = s(z)(p(z))k where s(z) is a regular function starlike with respect to the origin for |z| < 1, k is a positive constant, and p(z) is a regular function with positive real part in |z| < 1. The class of close-to-star functions introduced by Reade ([4]) is equivalent to C(1). In this paper we define the class C(k, A,B) (−1 £ B < A £ 1, k is positive constant) which contains the functions of the form f(z) = s(z)(p(z))k where s(z) is a regular Janowski starlike function, and p(z) is a regular functionwith positive real part in |z| < 1. The aim of this paper is to give some propertiesand distortion theorems for this class. Mathematics Subject Classification (2010): 30C45. Keywords: Distortion theorem, radius of starlikeness. |
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