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- W3476741 abstract "Let $mathcal{A}$ denote the class of normalized analytic functions in the unit disc $ U $ and $ P_{gamma} (alpha, beta) $ consists of $ f in mathcal{A} $ so that$ exists ~eta in mathbb{R}, quad Re bigg {e^{ieta} bigg [(1-gamma) Big (frac{f(z)}{z}Big )^{alpha}+ gamma frac{zf'(z)}{f(z)} Big (frac{f(z)}{z}Big )^{alpha} - betabigg ]bigg } > 0. $ In the present paper we shall investigate the integral transform$ V_{lambda, alpha}(f)(z) = bigg {int_{0}^{1} lambda(t) Big (frac{f(tz)}{t}Big )^{alpha}dtbigg }^{frac{1}{alpha}}, $ where $ lambda $ is a non-negative real valued function normalized by $ int_{0}^{1}lambda(t) dt=1 $. Actually we aim to find conditions on the parameters $ alpha, beta, gamma, beta_{1}, gamma_{1} $ such that $ V_{lambda, alpha}(f) $ maps $ P_{gamma}(alpha, beta) $ into $ P_{gamma_{1}}(alpha, beta_{1}) $. As special cases, we study various choices of $ lambda(t) $, related to classical integral transforms." @default.
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- W3476741 date "2008-12-01" @default.
- W3476741 modified "2023-09-30" @default.
- W3476741 title "Geometric properties of some linear operators defined by convolution" @default.
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- W3476741 doi "https://doi.org/10.5556/j.tkjm.39.2008.6" @default.
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