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Let f(z) = z +∑n=2∞anzn be analytic in the unit disk with the second coefficient a2 satisfying a2 = 2b, 0≤b≤1. Sharp radius of Janowski starlikeness is obtained for functions f whose nth coefficient satisfies an≤cn+d  (c,d≥0) or an≤c/n  (c>0  and  n≥3). Other radius constants are also obtained for these functions, and connections with earlier results are made.