由Hurwitz-Lerch ζ函数定义的p叶亚纯函数类的性质
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摘要
研究了由Srivastava-Attiya算子定义的一些p叶亚纯函数类,利用微分从属的方法,得到了相关函数类的包含性质、卷积性质、系数估计、偏差定理、积分性质以及从属性质等.
The main purpose of this paper is to investigate some subclasses of p-valent meromorphic functions involving the Srivastava-Attiya operator. By using the methods of differential subordination, Such results as inclusion relationships, convolution properties, coefficient inequalities, distortion theorem, integral-preserving properties and subordination are proved.
The main purpose of this paper is to investigate some subclasses of p-valent meromorphic functions involving the Srivastava-Attiya operator. By using the methods of differential subordination, Such results as inclusion relationships, convolution properties, coefficient inequalities, distortion theorem, integral-preserving properties and subordination are proved.
引文
[1] Srivastava H M, Choi J. Series associated with the Zeta and related functions[M]. Dordrecht, Boston,London:Kluwer Academic Publishers, 2001.
[2] Erdelyi A, Mangnus W, Oberhettinger F, Tricomi F G. Higher transcendental functions, vol 1[M].New York:McGraw-Hill, 1953.
[3] Srivastava H M, Choi J. Series associated with the zeta and related functions[M]. Dordrecht:Kluwer Academic Publishers, 2001.
[4] Soni A, Kant S, Prajapat J K. Strong differential subordination and superordination for multivalently meromorphic functions involving the hurwitz-lerch zeta function[J]. Proceedings of the National Academy of Sciences, India-Section A, 2015, 85(3):385-393.
[5] Eenigenburg P J, Mocanu P T, Miller S S, et al. On a briot-bouquet differential subordination[J].Revue Roumaine Des Mathematiques Pures Et Appliquees, 1984, 29(7):339-348.
[6] Whittaker E T, Watson G N. A course of modern analysis. Cambridge:Cambridge University Press. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, Reprint of the fourth[M]//A course of modern analysis:an introduction to the general theory of infinite processes and of analytic functions:with an account of the principal transcendental functions. Cambridge University Press, 1996:531.
[7] Wilken D R, Feng J. A remark on convex and starlike functions[J]. Journal of the London Mathematical Societ-Second Series, 1980, 21(2):287-290.
[8] Goodman A W. Univalent Functions, Vol.I[M]. Polygonal publishing House, Washington:New Jersey, 1983.
[9] Miller S S, Mocanu PT. Differential subordination and univalent functions[J]. Michigan Math J,1981, 28:157-171.
[2] Erdelyi A, Mangnus W, Oberhettinger F, Tricomi F G. Higher transcendental functions, vol 1[M].New York:McGraw-Hill, 1953.
[3] Srivastava H M, Choi J. Series associated with the zeta and related functions[M]. Dordrecht:Kluwer Academic Publishers, 2001.
[4] Soni A, Kant S, Prajapat J K. Strong differential subordination and superordination for multivalently meromorphic functions involving the hurwitz-lerch zeta function[J]. Proceedings of the National Academy of Sciences, India-Section A, 2015, 85(3):385-393.
[5] Eenigenburg P J, Mocanu P T, Miller S S, et al. On a briot-bouquet differential subordination[J].Revue Roumaine Des Mathematiques Pures Et Appliquees, 1984, 29(7):339-348.
[6] Whittaker E T, Watson G N. A course of modern analysis. Cambridge:Cambridge University Press. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, Reprint of the fourth[M]//A course of modern analysis:an introduction to the general theory of infinite processes and of analytic functions:with an account of the principal transcendental functions. Cambridge University Press, 1996:531.
[7] Wilken D R, Feng J. A remark on convex and starlike functions[J]. Journal of the London Mathematical Societ-Second Series, 1980, 21(2):287-290.
[8] Goodman A W. Univalent Functions, Vol.I[M]. Polygonal publishing House, Washington:New Jersey, 1983.
[9] Miller S S, Mocanu PT. Differential subordination and univalent functions[J]. Michigan Math J,1981, 28:157-171.