与贝努利双纽线和共轭点有关的一类解析函数的三阶Hankel行列式
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摘要
主要研究了与贝努利双纽线有关且具有共轭点的一类解析函数SL_c~*的阶Hankel行列式H_3(1),得到其上界估计.
In this paper, we investigate the Hankel determinant H_3(1) for a class of analytic functions SL_c~* associated with lemniscate of Bernoulli and conjugate points and obtain the upper bound of the above determinant.
In this paper, we investigate the Hankel determinant H_3(1) for a class of analytic functions SL_c~* associated with lemniscate of Bernoulli and conjugate points and obtain the upper bound of the above determinant.
引文
[1] Graham I, Kohr G. Geometric function theory in one and higher dimensions[M]. Marcel Dekker New York NY, USA, 2003.
[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] Sokol J, Stankiewicz J. Radius of convexity of some subclasses of strongly starlike functions[J]. Zesz Nauk Politech Rzeszowskiej Mat, 1996, 19(19):101-105.
[4] Ali R M, Cho N E, Ravichandran V, Kumar S S. Differential subordination for functions associated with the lemniscate of Bernoulli[J]. Taiwan J Math, 2012, 16(3):1017-1026.
[5] Sokol J. Coefficient estimates in a class of strongly starlike functions[J]. Kyungpook Math J, 2009,49(2):349-353.
[6] 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.
[7] Fekete M, Szeg(o|¨)G. Eine benberkung uber ungerada schlichte funktionen[J]. J London Math Soc,1933, 8(2):85-89.
[8] 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.
[9] Singh G. Hankel determinant for new subclasses of analytic functions with respect to symmetric points[J]. Int. J. of Modern Mathematical Sciences, 2013, 5(2):67-76.
[10] Sudharsan T V, Vijayalakshmi S P. Adolf Stephen B. Third Hankel determinant for a subclass of analytic univalent functions[J]. Malaya J Mat, 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] Raza M, Malik S N. Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of bernoulli[J]. Journal of Inequalities and Applications, 2013, 2013(1):1-8.
[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] Sokol J, Stankiewicz J. Radius of convexity of some subclasses of strongly starlike functions[J]. Zesz Nauk Politech Rzeszowskiej Mat, 1996, 19(19):101-105.
[4] Ali R M, Cho N E, Ravichandran V, Kumar S S. Differential subordination for functions associated with the lemniscate of Bernoulli[J]. Taiwan J Math, 2012, 16(3):1017-1026.
[5] Sokol J. Coefficient estimates in a class of strongly starlike functions[J]. Kyungpook Math J, 2009,49(2):349-353.
[6] 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.
[7] Fekete M, Szeg(o|¨)G. Eine benberkung uber ungerada schlichte funktionen[J]. J London Math Soc,1933, 8(2):85-89.
[8] 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.
[9] Singh G. Hankel determinant for new subclasses of analytic functions with respect to symmetric points[J]. Int. J. of Modern Mathematical Sciences, 2013, 5(2):67-76.
[10] Sudharsan T V, Vijayalakshmi S P. Adolf Stephen B. Third Hankel determinant for a subclass of analytic univalent functions[J]. Malaya J Mat, 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] Raza M, Malik S N. Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of bernoulli[J]. Journal of Inequalities and Applications, 2013, 2013(1):1-8.