Bull. Korean Math. Soc. 2015; 52(3): 1035-1046
Printed May 31, 2015
https://doi.org/10.4134/BKMS.2015.52.3.1035
Copyright © The Korean Mathematical Society.
Nihat Ya\u{g}mur
Erzincan University
In this work we present some geometric properties (like starlikeness and convexity of order $\alpha $ and also close-to-convexity of order $(1+\alpha )/2$) for normalized of Lommel functions of the first kind. In order to prove our main results, we use the technique of differential subordinations and some inequalities. Furthermore, we present some applications of convexity involving Lommel functions associated with the Hardy space of analytic functions, i.e., we obtain conditions for the function $h_{\mu ,v}(z) $ to belong to the Hardy space $\mathcal{H}^{p}.$
Keywords: analytic function, Lommel functions, Hardy space
MSC numbers: Primary 30C45; Secondary 33C10
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