Differential Subordinations Involving Generalized Bessel Functions

Abstract

In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some appropriate classes of admissible functions. We obtain also some sandwich-type results and we point out various known or new special cases of our main results.Comment: 15 pages, accepted in Bulletin of the Malaysian Mathematical Sciences Societ

Majorization problems for classes of analytic functions

“…see the work of [1,2,3]). Using the B c m − linear operator due to Baricz et al [3] given by (1.6), we now define the following new subclass of A.…”

Lemniscate convexity of generalized Bessel functions

“…Baricz et al [2] obtained sufficient conditions on the constants α > −1 and β such that the function z/u p,b,c (z) ∈ S(α, β, λ). Prajapat [14] determined conditions for generalized bessel function (with a different normalization that one considered in this paper) to be univalent in the open unit disk.…”

Third-Order Differential Superordination Involving the Generalized Bessel Functions

“…Recently, Deniz et al [16] and Deniz [15] (see also [8][9][10][11]23] and [30]) considered the function ϕ p,b,c (z) defined, in terms of the generalized Bessel function ω p,b,c (z) in Eq. (1.3), by the following transformation:…”

“…Baricz et al [10] (see also [33]) introduced a new operator B c κ : A → A, which is defined by means of the Hadamard product (or convolution) as follows:…”