THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS

doi:10.1016/S0252-9602(14)60116-8

Abstract

Abstract:

In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as
z(B^c_K₊₁f(z))′ = KB^c_Kf(z) − (K − 1)B^c_K+1f(z),

where b, c, p ∈ C and K = p + (b + 1)/2∈ C \ Z ⁻₀ (Z ⁻₀ = {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.

Key words: differential subordination, univalent functions, Hadamard product, admissible functions, generalized Bessel functions

CLC Number:

30C45

TANG Huo, Erhan DENIZ. THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS[J].Acta mathematica scientia,Series B, 2014, 34(6): 1707-1719.

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