The main purpose of this paper is to determine the radii of starlikeness and convexity of the generalized k−Bessel functions for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. The characterization of entire functions from Laguerre-Pólya class plays an crucial role in this paper. Moreover, the interlacing properties of the zeros of k−Bessel function and its derivative is also useful in the proof of the main results. By making use of the Euler-Rayleigh inequalities for the real zeros of the generalized k−Bessel function, we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero.

In this investigation our main aim is to determine the radii of uniform convexity of selected normalized q -Bessel and Wright functions. Here we consider six different normalized forms of q -Bessel functions and we apply three different kinds of the normalization of the Wright function. We also show that the obtained radii are the smallest positive roots of some functional equations.

The main purpose of the present paper is to ascertain the radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function,, the respective M−radii, which are represented by r ⋆ A,B (f ) and r c A,B (f ), are called as the radii of Janowski starlikeness and Janowski convexity. These are respectively the largest r with 0 ≤ r ≤ 1 such that< 1 (|z| < r).

In this paper we introduce and study some properties of k-bi-starlike functions defined by making use of the Sȃlȃgean derivative operator. Upper bounds on the second Hankel determinant for k-bi-starlike functions are investigated. Relevant connections of the results presented here with various well-known results are briefly indicated.

In this paper we deal with the radii of starlikeness and convexity of the q -Mittag-Leffler function for three different kinds of normalization by making use of their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays a pivotal role in this investigation.