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.

参考文献

[1] Ali R M, Ravichandran V, Seenivasagan N. Subordination and superordination on Schwarzian derivatives. J Ineq Appl, 2008, 2008: Article ID 12328

[2] Ali R M, Ravichandran V, Seenivasagan N. Subordination and superordination of the Liu-Srivastava linear operator on meromorphic functions. Bull Malays Math Sci Soc, 2008, 31(2): 193–207

[3] Ali R M, Ravichandran V, Seenivasagan N. Differential subordination and superordination of analytic functions defined by the multiplier transformation. Math Inequal Appl, 2009, 12(1): 123–139

[4] Ali R M, Ravichandran V, Seenivasagan N. Differential subordination and superordination of analytic functions defined by the Dziok-Srivastava operator. J Franklin Inst, 2010, 347(9): 1762–1781

[5] Ali R M, Ravichandran V, Seenivasagan N. On subordination and superordination of the multiplier trans-formation for meromorphic functions. Bull Malays Math Sci Soc, 2010, 33(2): 311–324

[6] Andras S, Baricz A. Monotonicity property of generalized and normalized Bessel functions of complex order. Complex Var Elliptic Equ, 2009, 54(7): 689–696

[7] Antonino J A, Miller S S. Third-order differential inequalities and subordinations in the complex plane. Complex Var Elliptic Equ, 2011, 56(5): 439–454

[8] Baricz A. Applications of the admissible functions method for some differential equations. Pure Appl Math, 2002, 13(4): 433–440

[9] Baricz A. Geometric properties of generalized Bessel functions. Publ Math Debrecen, 2008, 73: 155–178

[10] Baricz A. Generalized Bessel Functions of the First Kind. Lecture Notes in Mathematics, Vol 1994. Berlin: Springer-Verlag, 2010

[11] Baricz A, Ponnusamy S. Starlikeness and covexity of generalized Bessel function. Integral Transform Spec Funct, 2010, 21(9): 641–651

[12] Cho N E, Kwon O S, Owa S, Srivastava H M. A class of integral operators preserving subordination and superordination for meromorphic functions. Appl Math Comput, 2007, 193: 463–474

[13] Cho N E, Srivastava H M. A class of nonlinear integral operators preserving subordination and superordi-nation. Integral Transforms Spec Funct, 2007, 18: 95–107

[14] Deniz E. Convexity of integral operators involving generalized Bessel functions. Integral Transforms Spec Funct, 2013, 24(3): 201–216

[15] Deniz E, Orhan H, Srivastava H M. Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions. Taiwansese J Math, 2011, 15(2): 883–917

[16] Dziok J, Srivastava H M. Classes of analytic functions associated with the generalized hypergeometric function. Appl Math Comput, 1999, 103(1): 1–13

[17] Dziok J, Srivastava H M. Certain subclasses of analytic functions associated with the generalized hyperge-ometric function. Integral Transform Spec Funct, 2003, 14(1): 7–18

[18] Miller S S, Mocanu P T. Univalence of Gaussian and confluent hypergeometric functions. Proc Amer Math Soc, 1990, 110(2): 333–342

[19] Miller S S, Mocanu P T. Differential Subordinations. Monographs and Textbooks in Pure and Applied Mathematics, 225. New York: Marcel Dekker, 2000

[20] Owa S, Srivastava H M. Univalent and starlike generalized hypergeometric functions. Canad J Math, 1987, 39(5): 1057–1077

[21] Ponnusamy S, Juneja O P. Third-order differential inequalities in the complex plane. Current Topics in Analytic Function Theory. Singapore, London: World Scientific, 1992

[22] Ponnusamy S, Ronning F. Geometric properties for convolutions of hypergeometric functions and functions with the derivative in a halfplane. Integral Transform Spec Funct, 1999, 8: 121–138

[23] Ponnusamy S, Vuorinen M. Univalence and convexity properties for confluent hypergeometric functions. Complex Var Theory Appl, 1998, 36(1): 73–97

[24] Ponnusamy S, Vuorinen M. Univalence and convexity properties for Gaussian hypergeometric functions. Rocky Mountain J Math, 2001, 31(1): 327–353

[25] Prajapat J K. Certain geometric properties of normalized Bessel Functions. Appl Math Lett, 2011, 24: 2133–2139

[26] Selinger V. Geometric properties of normalized Bessel functions. Pure Math Appl, 1995, 6: 273–277

[27] Shanmugam T N, Sivasubramanian S, Srivastava H M. Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations. Integral Transforms Spec Funct, 2006, 17: 889–899

[28] Srivastava H M, Yang D G, Xu N E. Subordinations for multivalent analytic functions associated with the Dziok-Srivastava operator. Integral Transforms Spec Funct, 2009, 20: 581–606

[29] Watson G N. A Treatise on the Theory of Bessel Functions. 2nd ed. Cambridge, London, New York: Cambridge University Press, 1944

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

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 9

Metrics

本文评价

推荐阅读 10

[1]	彭志刚, 钟广祯. SOME PROPERTIES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL INEQUALITIES[J]. 数学物理学报(英文版), 2017, 37(1): 69-78.
[2]	H. M. SRIVASTAVA, S. GABOURY, F. GHANIM. INITIAL COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS[J]. 数学物理学报(英文版), 2016, 36(3): 863-871.
[3]	Samaneh Gholizadeh HAMIDI, Suzeini Abdul HALIM, Janusz SOKóL. STARLIKENESS AND SUBORDINATION PROPERTIES OF A LINEAR OPERATOR[J]. 数学物理学报(英文版), 2014, 34(5): 1446-1460.
[4]	Mohamed K. AOUF, Teodor BULBOACA, Tamer M. SEOUDY. CERTAIN FAMILY OF INTEGRAL OPERATORS PRESERVING SUBORDINATION AND SUPERORDINATION[J]. 数学物理学报(英文版), 2014, 34(4): 1166-1178.
[5]	Mohamed K. AOUF, Teodor BULBOACA, Rabha M. EL-ASHWASH. SUBORDINATION PROPERTIES OF MULTIVALENT FUNCTIONS INVOLVING AN EXTENDED FRACTIONAL DIFFERINTEGRAL OPERATOR[J]. 数学物理学报(英文版), 2014, 34(2): 367-379.
[6]	Jacek DZIOK\|Ravinder Krishna RAINA\|Janusz SOKóL. DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS[J]. 数学物理学报(英文版), 2013, 33(3): 609-620.
[7]	S. HUSSAIN, J. SOKóL. ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR[J]. 数学物理学报(英文版), 2012, 32(4): 1399-1407.
[8]	J. Dziok. CLASSES OF MEROMORPHIC FUNCTIONS ASSOCIATED WITH CONIC REGIONS[J]. 数学物理学报(英文版), 2012, 32(2): 765-774.
[9]	J. Dziok . A UNIFIED CLASS OF ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS[J]. 数学物理学报(英文版), 2011, 31(4): 1357-1366.