Bounded starlike functions of complex order |
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Authors: | M A Nasr M K Aouf |
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Affiliation: | 1. Kingdom of Saudi Arabia, T. T. Junior College, P.O. Box. 2375, Dammam 2. Faculty of Science, University of Mansoura, Mansoura, Egypt
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Abstract: | LetF(b, M) (b ≠ 0 complex,M>1/2) denote the class of functionsf(z) =z + Σ n=2 ∞ a n z n analytic in U={z:|z|<1} which satisfy for fixedM, f(z)/z ≠ 0 inU and (left| {frac{{b - 1 + left[ {zf'{{left( z right)} mathord{left/ {vphantom {{left( z right)} {fleft( z right)}}} right. kern-0em} {fleft( z right)}}} right]}}{b} - M} right|< M, z in U) . In this note we obtain various representations for functions inF(b, M). We maximize |a3=μa 2 2 | over the classF(b, M). Also sharp coefficient bounds are established for functions inF(b, M). We also obtain the sharp radius of starlikeness of the classF(b, M). |
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