In this paper we determine the radius of convexity for three kind of
normalized Bessel functions of the first kind. In the mentioned cases the
normalized Bessel functions are starlike-univalent and convex-univalent,
respectively, on the determined disks. The key tools in the proofs of the main
results are some new Mittag-Leffler expansions for quotients of Bessel
functions of the first kind, special properties of the zeros of Bessel
functions of the first kind and their derivative, and the fact that the
smallest positive zeros of some Dini functions are less than the first positive
zero of the Bessel function of the first kind. Moreover, we find the optimal
parameters for which these normalized Bessel functions are convex in the open
unit disk. In addition, we disprove a conjecture of Baricz and Ponnusamy
concerning the convexity of the Bessel function of the first kind.Comment: 16 pages; an error has been correcte
In the present investigation, we consider two new subclasses N?? (?, ?) and N?? (?, ?) of bi?univalent functions defined in the open unit disk u = {z : |z| < 1}. Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.
In the present work our object is to establish some geometric properties (like univalence, starlikeness, convexity and close-to-convexity) for the generalized Struve functions. In order to prove our main results, we use the technique of differential subordinations developed by Miller and Mocanu, some inequalities, and some classical results of Ozaki and Fejer.Mathematics Subject Classification 2010: 30C45, 33C10.
Abstract. In the present investigation the authors obtain upper bounds for the second Hankel determinant H 2 (2) of the classes bi-starlike and bi-convex functions of order β, represented by S * σ (β) and Kσ(β), respectively. In particular, the estimates for the second Hankel determinant H 2 (2) of bi-starlike and bi-convex functions which are important subclasses of bi-univalent functions are pointed out.
Abstract. Geometric properties of the classical Lommel and Struve functions, both of the first kind, are studied. For each of them, there different normalizations are applied in such a way that the resulting functions are analytic in the unit disc of the complex plane. For each of the six functions we determine the radius of starlikeness precisely.
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