Nihat Yagmur

Starlikeness and Convexity of Generalized Struve Functions

We give sufficient conditions for the parameters of the normalized form of the generalized Struve functions to be convex and starlike in the open unit disk.

Radii of starlikeness of some special functions

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.

Geometric properties of some Lommel and Struve functions

In this paper our aim is to deduce some new results on the zeros of the derivatives of some Lommel and Struve functions of the first kind and to apply these results in order to determine the radii of convexity of some normalized Lommel and Struve functions of the first kind.The radii of convexity of some Lommel and Struve functions of the first kind are determined. For both of Lommel and Struve functions three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane. Some results on the zeros of the derivatives of some Lommel and Struve functions of the first kind are also deduced, which may be of independent interest.

Hardy space of generalized Struve functions

In this paper, we present some immediate applications of convexity involving Struve functions associated with the Hardy space of analytic functions, i.e. we obtain conditions for the functionto belong to the Hardy space

Close-to-convexity of normalized Dini functions

In this paper necessary and sufficient conditions are deduced for the close-to-convexity of some special combinations of Bessel functions of the first kind and their derivatives by using a result of Shah and Trimble about transcendental entire functions with univalent derivatives and some newly discovered Mittag–Leffler expansions for Bessel functions of the first kind.

Coefficient estimates for Sakaguchi type functions

Let S λ,μ(α, t) be the class of normalized analytic functions defined in the open unit disk satisfying R ( (1− t)z ( D λ,μf(z) )′ D λ,μf(z)−D λ,μf(tz) ) > α, |t| ≤ 1, t = 1 for some α(0 ≤ α < 1) and D λ,μ is a linear multiplier differential operator defined by the authors in [2]. The object of the present paper is to discuss some properties of functions f(z) belonging to the classes S λ,μ(α, t) and T n λ,μ(α, t) where f(z) ∈ T λ,μ(α, t) if and only if zf ′(z) ∈ S λ,μ(α, t).