Author： HO CHOI JAE
Publisher： Taylor & Francis Ltd
ISSN： 1065-2469
Source： Integral Transforms and Special Functions, Vol.13, Iss.2, 2002-01, pp. : 117-130
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Abstract
Let <$>{cal A}<$> be the class of normalized analytic functions in the unit disk <$>{cal U}<$> and define the class <$$>{cal P}_{gamma}(beta) = left{f in {cal A} vert exists varphi in {bf R} vert hbox{Re} bigg{ e^{ivarphi} left((1-gamma) ,{,f(z) over z} + gamma f^{prime}(z) - beta}right)bigg} gt 0, ; z in {cal U} bigg }. For a function <$>f in {cal P}_{gamma}(beta)<$> and the Gaussian hypergeometric function <$>_{2}F_{1} (a,b;c;z)<$>, we investigate the convexity and starlikeness for the convolution operator <$>H_{a,b,c}<$> defined by <$$>H_{a,b,c} (f)(z) = z ; {_{2} F_{1}} (a,b;c;z) ast f(z).
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