一类解析函数的三阶Hankel行列式
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摘要
主要研究一类解析函数Rτγ(A,B)的三阶Hankel行列式H3(1),得到其上界估计,并推广了已有的结果.
In this paper,we investigate the Hankel determinant H3( 1) for a class of analytic functions denoted by Rτγ( A,B),and obtain the upper bound of the above determinant,which generalize some existing results.
In this paper,we investigate the Hankel determinant H3( 1) for a class of analytic functions denoted by Rτγ( A,B),and obtain the upper bound of the above determinant,which generalize some existing results.
引文
[1]MILLER S S,MOCANU P T. Differential Subordinations:Theory and Applications[M]. New York:Marcel Dekker Incorporated,2000.
[2]BANSAL D. Upper bound of second Hankel determinant for a new class of analytic functions[J]. Applied Mathematics Letters,2013,26(1):103-107.
[3]NOONAN J W,THOMAS D K. On the second Hankel determinant of areally mean p-valent functions[J]. Transactions of the American Mathematical Society,1976,223(2):337-346.
[4]FEKETE M,SZEGG. Eine benberkung uber ungerada schlichte funktionen[J]. J London Math Soc,1933,8(2):85-89.
[5]LIU M S,XU J F,YANG M. Upper bound of second Hankel determinant for certain subclasses of analytic functions[J]. Abstract and Applied Analysis,2014,2014(1):1-10.
[6]SINGH G. Hankel determinant for new subclasses of analytic functions with respect to symmetric points[J]. Int J Modern Mathematical Sciences,2013,5(2):67-76.
[7]KEONG S L,RAVICHANDRAN V,SUPRAMANIAML S. Bounds for the second Hankel determinant of certain univalent functions[J]. J Inequalities and Applications,2013,2013(1):281-298.
[8]JANTENG A,ABDUL H S,DARUS M. Hankel determinant for starlike and convex functions[J]. Int J Math Analysis,2007,13(1):619-625.
[9]RAZA M,MALIK S N. Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of bernoulli[J]. J Inequalities and Applications,2013,2013(1):1-8.
[10]SUDHARSAN T V,VIJAYALAKSHMI S P,ADOLF S B. Third Hankel determinant for a subclass of analytic univalent functions[J]. Malaya J Math,2014,2(4):438-444.
[11]BANSAL D,MAHARANA S,PRAJAPAT J K. Third order Hankel determinant for certain univalent functions[J]. J Korean Math Soc,2015,52(6):1139-1148.
[12]张海燕,汤获,马丽娜.与共轭点有关的一类解析函数的三阶Hankel行列式[J].应用泛函分析学报,2017,19(3):279-286.
[13]张海燕,汤获,马丽娜.一类解析函数的三阶Hankel行列式上界估计[J].纯粹数学与应用数学,2017,33(2):211-220.
[14]张海燕,马丽娜,王焕.某类具有对称共轭点的倒星象函数的三阶Hankel行列式上界估计[J].纯粹数学与应用数学,2017,33(5):503-512.
[15]DUREN P L. Univalent Functions,Grundlehren der Mathematischen Wissenschaften[M]. New York:Springer-Verlag,1983:162-205.
[16]LIBERA R J,ZLOTKIEWICZ E J. Coefficients bounds for the inverse of a function with derivative in P[J]. Proc Am Math Soc,1983,87(2):251-257.
[2]BANSAL D. Upper bound of second Hankel determinant for a new class of analytic functions[J]. Applied Mathematics Letters,2013,26(1):103-107.
[3]NOONAN J W,THOMAS D K. On the second Hankel determinant of areally mean p-valent functions[J]. Transactions of the American Mathematical Society,1976,223(2):337-346.
[4]FEKETE M,SZEGG. Eine benberkung uber ungerada schlichte funktionen[J]. J London Math Soc,1933,8(2):85-89.
[5]LIU M S,XU J F,YANG M. Upper bound of second Hankel determinant for certain subclasses of analytic functions[J]. Abstract and Applied Analysis,2014,2014(1):1-10.
[6]SINGH G. Hankel determinant for new subclasses of analytic functions with respect to symmetric points[J]. Int J Modern Mathematical Sciences,2013,5(2):67-76.
[7]KEONG S L,RAVICHANDRAN V,SUPRAMANIAML S. Bounds for the second Hankel determinant of certain univalent functions[J]. J Inequalities and Applications,2013,2013(1):281-298.
[8]JANTENG A,ABDUL H S,DARUS M. Hankel determinant for starlike and convex functions[J]. Int J Math Analysis,2007,13(1):619-625.
[9]RAZA M,MALIK S N. Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of bernoulli[J]. J Inequalities and Applications,2013,2013(1):1-8.
[10]SUDHARSAN T V,VIJAYALAKSHMI S P,ADOLF S B. Third Hankel determinant for a subclass of analytic univalent functions[J]. Malaya J Math,2014,2(4):438-444.
[11]BANSAL D,MAHARANA S,PRAJAPAT J K. Third order Hankel determinant for certain univalent functions[J]. J Korean Math Soc,2015,52(6):1139-1148.
[12]张海燕,汤获,马丽娜.与共轭点有关的一类解析函数的三阶Hankel行列式[J].应用泛函分析学报,2017,19(3):279-286.
[13]张海燕,汤获,马丽娜.一类解析函数的三阶Hankel行列式上界估计[J].纯粹数学与应用数学,2017,33(2):211-220.
[14]张海燕,马丽娜,王焕.某类具有对称共轭点的倒星象函数的三阶Hankel行列式上界估计[J].纯粹数学与应用数学,2017,33(5):503-512.
[15]DUREN P L. Univalent Functions,Grundlehren der Mathematischen Wissenschaften[M]. New York:Springer-Verlag,1983:162-205.
[16]LIBERA R J,ZLOTKIEWICZ E J. Coefficients bounds for the inverse of a function with derivative in P[J]. Proc Am Math Soc,1983,87(2):251-257.