TAILIEUCHUNG - Some radius problem for certain families of analytic functions

The aim of this paper is to give bounds of the radius of α convexity for certain families of analytic functions in the unit disc. The radius of α-convexity is generalization of the radius of convexity and the radius of starlikeness, and introduced by , and | Turk J Math 24 (2000) , 401 – 412. ¨ ITAK ˙ c TUB Some Radius Problem for Certain Families of Analytic Functions Ya¸sar Polato˘glu, Metin Bolcal Abstract The aim of this paper is to give bounds of the radius of α-convexity for certain families of analytic functions in the unit disc. The radius of α-convexity is generalization of the radius of convexity and the radius of starlikeness, and introduced by ; and [3,4] Key Words: Subordination principle, Carathedory functions, Janowski Starlike functions, Starlike functions of order β, The radius of Starlikeness, The radius of convexity, The radius of α-convexity. 1. Introduction Most radius problems lead to functions p(z) with positive real part, or some more restrictive condition Re p(z). Therefore, for our study we shall need the following definitions and the subordination principle. Subordination Principle: Let g(z) and f(z) be regular and analytic in D = {z

• Toán học
• Subordination principle
• Carathedory functions
• Janowski Starlike functions
• Starlike functions of order β
• The radius of Starlikeness
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