Hardy Space of Lommel Functions

Abstract

Abstract. In this work we present some geometric properties (like starlikeness and convexity of order α and also close-to-convexity of order (1 + α)/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 hµ,v(z) to belong to the Hardy space H p .

Certain Geometric Properties of Generalized Dini Functions

“…Baricz [2] uses the idea of Ponnusamy and found the Hardy spaces of Bessel functions while Yag mur and Orhan [10] studied the same problem for generalized Struve functions. Similarly Yag mur [22] studied the problem for Lommel functions and Raza et al [9] studied the same problem for Wright functions. To prove our main results we need the following lemmas.…”

On some geometric properties and Hardy class of <i>q</i>-Bessel functions

“…Furthermore, Eenigenburg and Keogh determined some conditions on the convex, starlike and close-to-convex functions to belong to the Hardy space H p in [10]. On the other hand, the authors in [7,16,17,22,23,28,29] studied the Hardy space of some special functions (like Hypergeometric, Bessel, Struve, Lommel and Mittag-Leffler) and analytic function families.…”

Lemniscate convexity of generalized Bessel functions

“…Yagmur [18] obtained conditions on the parameters µ and p such that the function satisfies Re(h µ,p (z)/z) > α for 0 ≤ α < 1. Baricz et al [7] studied the zeroes of some normalization of Lommel and Struve function and hence determined the radius of convexity of these functions.…”