doiSerbia

Radii of starlikeness and convexity for functions with fixed second coefficient defined by subordination

Ali Rosihan M. (School of Mathematical Sciences, Universiti Sains Malaysia, USM Penang, Malaysia)
Cho Eun Nak (Department of Applied Mathematics, Pukyong National University, Busan, South Korea)
Jain Kumar Naveen (Department of Mathematics, University of Delhi, Delhi, India)
Ravichandran V. (Department of Mathematics, University of Delhi, Delhi, India + School of Mathematical Sciences, Universiti Sains Malaysia, USM Penang, Malaysia)

Several radii problems are considered for functions f (z) = z + a2z2 + ... with fixed second coefficient a2. For 0 ≤ β < 1, sharp radius of starlikeness of order β for several subclasses of functions are obtained. These include the class of parabolic starlike functions, the class of Janowski starlike functions, and the class of strongly starlike functions. Sharp radius of convexity of order β for uniformly convex functions, and sharp radius of strong-starlikeness of order γ for starlike functions associated with the lemniscate of Bernoulli are also obtained as special cases.

Keywords: Subordination, radius of starlikeness, radius of convexity, radius of strong starlikeness, lemniscate of Bernoulli