Third-order differential subordination results for analytic functions involving the generalized Bessel functions

In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bκcf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z(Bκ+1cf(z))′ = κBκcf(z) - (κ - 1) Bκ+1cf(z)where b,c,p   ℂ and κ = p + (b+1)/2 ∈ C\(Z0- = {0, -1, -2,⋯}). The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.