由微分算子定义的双单叶函数类的系数估计
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摘要
利用一类普通算子定义单位圆盘U内的双单叶解析函数类MNhΣ,p(λ,μ; m,δ),并研究它的泰勒展式中第2项与第3项系数的估计结果,推广了众多已知文献的结论.
In this paper,a familiar subclass MNhΣ,p( λ,μ; m,δ) of analytic and bi-univalent functions in the open unit disk U defined by a general differential operator are introduced and investigated. Estimates for the second and third coefficients of their Taylor expansion are obtained. Some relevant connections of the result presented here with various well-known results are briefly indicated.
In this paper,a familiar subclass MNhΣ,p( λ,μ; m,δ) of analytic and bi-univalent functions in the open unit disk U defined by a general differential operator are introduced and investigated. Estimates for the second and third coefficients of their Taylor expansion are obtained. Some relevant connections of the result presented here with various well-known results are briefly indicated.
引文
[1]SRIVASTAVA H M,MISHRA A K,GOCHHAYAT P. Certain subclasses of analytic and bi-univalent functions[J]. Appl Math Lett,2010,23(10):1188-1192.
[2]石磊,王智刚.两类双单叶非Bazilevic函数族的系数估计[J].安徽大学学报(自然科学版),2016,40(3):17-21.
[3]GOYAL S P,GOSWAMI P. Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives[J]. J Egyptian Math Soc,2012,20(3):179-182.
[4]LI X F,WANG A P. Two new subclasses of bi-univalent functions[J]. Int Math Forum,2012,7:1495-1504.
[5]PENG Z G,HAN Q Q. On the coefficients of several classes of bi-univalent functions[J]. Acta Math Sci,2014,34(1):228-240.
[6]BULUT S. Coefficient estimates for a class of analytic and biunivalent functions[J]. Novi Sad J Math,2013,43(2):59-65.
[7]熊良鹏.双单叶星形和凸函数的系数边界[J].西南师范大学学报(自然科学版),2015,40(6):5-10.
[8]熊良鹏,田琳,李小飞.基于Salagean算子的bi单叶函数系数估计[J].数学的实践与认识,2015,45(3):219-223.
[9]都俊杰,邹发伟,秦川,等.一类利用从属关系定义的复数阶双单叶函数类的系数问题[J].四川师范大学学报(自然科学版),2016,39(3):344-348.
[10]李小飞,秦川.一类利用从属关系定义的双单叶函数类[J].四川师范大学学报(自然科学版),2014,37(4):511-514.
[11]秦川,冯建中,李小飞. Pascu类亚纯双单叶函数的系数估计[J].四川师范大学学报(自然科学版),2016,39(3):349-353.
[12]CHEN F,LI X.Coefficient bounds for a new subclass of bi-univalent functions defined by salagean operator[J]. J Math Research Appl,2017,37(3):290-298.
[13]CAGLAR M,ORHAN H,YAGMUR N. Coefficient bounds for new subclasses of bi-univalent functions[J]. Filomat,2013,27(7):1165-1171.
[14]FRASIN B A,AOUF M K. New subclasses of bi-univalent functions[J]. Appl Math Lett,2011,24(9):1569-1573.
[15]SRIVASTAVA H M,BULUT S. Coefficient estimates for a general subclass of analytic and bi-univalent functions[J]. Filomat,2013,27(5):831-842.
[16] AL-OBOUDI F M. On univalent functions defined by a generalized Salagean operator[J]. Int J Math Math Sci,2004,27:1429-1436,doi:10.1155/S0161171204108090.
[17]TANG H,DENG G T,LI S H. Coefficient estimates for new subclasses of Ma-Minda bi-univalent functions[J]. J Inequ Appl,2013,317(1):1-10.
[18]BULUT S. Coefficient estimates for new subclasses of analytic and bi-univalent functions defined by Al-Oboudi differential operator[J]. J Function Spaces Appl,2013,ID181932.
[19]ALTINKAYA S,YALCIN S. Coefficient estimates for a certain subclass of analytic and bi-univalent functions[J]. Acta Universitatis Apulensis,2014,40:347-354.
[20]PORWAL S,DARUS M. On a new subclass of bi-univalent functions[J]. J Egyptian Math Soc,2013,21(3):190-193.
[21]XU Q H,XIAO H G,SRIVASTAVA H M. A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems[J]. Appl Math Comput,2012,218:11461-11465.
[2]石磊,王智刚.两类双单叶非Bazilevic函数族的系数估计[J].安徽大学学报(自然科学版),2016,40(3):17-21.
[3]GOYAL S P,GOSWAMI P. Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives[J]. J Egyptian Math Soc,2012,20(3):179-182.
[4]LI X F,WANG A P. Two new subclasses of bi-univalent functions[J]. Int Math Forum,2012,7:1495-1504.
[5]PENG Z G,HAN Q Q. On the coefficients of several classes of bi-univalent functions[J]. Acta Math Sci,2014,34(1):228-240.
[6]BULUT S. Coefficient estimates for a class of analytic and biunivalent functions[J]. Novi Sad J Math,2013,43(2):59-65.
[7]熊良鹏.双单叶星形和凸函数的系数边界[J].西南师范大学学报(自然科学版),2015,40(6):5-10.
[8]熊良鹏,田琳,李小飞.基于Salagean算子的bi单叶函数系数估计[J].数学的实践与认识,2015,45(3):219-223.
[9]都俊杰,邹发伟,秦川,等.一类利用从属关系定义的复数阶双单叶函数类的系数问题[J].四川师范大学学报(自然科学版),2016,39(3):344-348.
[10]李小飞,秦川.一类利用从属关系定义的双单叶函数类[J].四川师范大学学报(自然科学版),2014,37(4):511-514.
[11]秦川,冯建中,李小飞. Pascu类亚纯双单叶函数的系数估计[J].四川师范大学学报(自然科学版),2016,39(3):349-353.
[12]CHEN F,LI X.Coefficient bounds for a new subclass of bi-univalent functions defined by salagean operator[J]. J Math Research Appl,2017,37(3):290-298.
[13]CAGLAR M,ORHAN H,YAGMUR N. Coefficient bounds for new subclasses of bi-univalent functions[J]. Filomat,2013,27(7):1165-1171.
[14]FRASIN B A,AOUF M K. New subclasses of bi-univalent functions[J]. Appl Math Lett,2011,24(9):1569-1573.
[15]SRIVASTAVA H M,BULUT S. Coefficient estimates for a general subclass of analytic and bi-univalent functions[J]. Filomat,2013,27(5):831-842.
[16] AL-OBOUDI F M. On univalent functions defined by a generalized Salagean operator[J]. Int J Math Math Sci,2004,27:1429-1436,doi:10.1155/S0161171204108090.
[17]TANG H,DENG G T,LI S H. Coefficient estimates for new subclasses of Ma-Minda bi-univalent functions[J]. J Inequ Appl,2013,317(1):1-10.
[18]BULUT S. Coefficient estimates for new subclasses of analytic and bi-univalent functions defined by Al-Oboudi differential operator[J]. J Function Spaces Appl,2013,ID181932.
[19]ALTINKAYA S,YALCIN S. Coefficient estimates for a certain subclass of analytic and bi-univalent functions[J]. Acta Universitatis Apulensis,2014,40:347-354.
[20]PORWAL S,DARUS M. On a new subclass of bi-univalent functions[J]. J Egyptian Math Soc,2013,21(3):190-193.
[21]XU Q H,XIAO H G,SRIVASTAVA H M. A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems[J]. Appl Math Comput,2012,218:11461-11465.