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

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

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (6): 1707-1719.doi: 10.1016/S0252-9602(14)60116-8

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

汤获|Erhan DENIZ

School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China；School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China； Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars, Turkey

收稿日期:2013-10-28 修回日期:2014-02-14 出版日期:2014-11-20 发布日期:2014-11-20
基金资助:
This work was partly supported by the Natural Science Foundation of China (11271045), the Higher School Doctoral Foundation of China (20100003110004), the Natural Science Foundation of Inner Mongolia of China (2010MS0117) and the Higher School Foundation of Inner Mongolia of China (NJZY13298) (to Tang); and by the Commission for the Scientific Research Projects of Kafkas Univertsity (2012-FEF-30) (to Deniz).

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

TANG Huo, Erhan DENIZ

School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China；School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China； Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars, Turkey

Received:2013-10-28 Revised:2014-02-14 Online:2014-11-20 Published:2014-11-20
Supported by:
This work was partly supported by the Natural Science Foundation of China (11271045), the Higher School Doctoral Foundation of China (20100003110004), the Natural Science Foundation of Inner Mongolia of China (2010MS0117) and the Higher School Foundation of Inner Mongolia of China (NJZY13298) (to Tang); and by the Commission for the Scientific Research Projects of Kafkas Univertsity (2012-FEF-30) (to Deniz).

摘要/Abstract

摘要：

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.

关键词: differential subordination, univalent functions, Hadamard product, admissible functions, generalized Bessel functions

Abstract:

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

中图分类号:

30C45

汤获, Erhan DENIZ. THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS[J]. 数学物理学报(英文版), 2014, 34(6): 1707-1719.

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

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

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