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Inclusion Properties for Certain Subclasses of Analytic Functions Associated with the Dziok-Srivastava Operator
Journal of Inequalities and Applications volume 2007, Article number: 051079 (2007)
Abstract
The purpose of the present paper is to introduce several new classes of analytic functions defined by using the Choi-Saigo-Srivastava operator associated with the Dziok-Srivastava operator and to investigate various inclusion properties of these classes. Some interesting applications involving classes of integral operators are also considered.
References
Owa S, Srivastava HM: Analytic solution of a class of Briot-Bouquet differential equations. In Current Topics in Analytic Function Theory. Edited by: Srivastava HM, Owa S. World Scientific, River Edge, NJ, USA; 1992:252–259.
Choi JH, Saigo M, Srivastava HM: Some inclusion properties of a certain family of integral operators. Journal of Mathematical Analysis and Applications 2002,276(1):432–445. 10.1016/S0022-247X(02)00500-0
Ma W, Minda D: An internal geometric characterization of strongly starlike functions. Annales Universitatis Mariae Curie-Skłodowska, Sectio A 1991, 45: 89–97.
Dziok J, Srivastava HM: Classes of analytic functions associated with the generalized hypergeometric function. Applied Mathematics and Computation 1999,103(1):1–13.
Dziok J, Srivastava HM: Some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function. Advanced Studies in Contemporary Mathematics 2002,5(2):115–125.
Dziok J, Srivastava HM: Certain subclasses of analytic functions associated with the generalized hypergeometric function. Integral Transforms and Special Functions 2003,14(1):7–18. 10.1080/10652460304543
Liu J-L, Srivastava HM: Certain properties of the Dziok-Srivastava operator. Applied Mathematics and Computation 2004,159(2):485–493. 10.1016/j.amc.2003.08.133
Liu J-L, Srivastava HM: Classes of meromorphically multivalent functions associated with the generalized hypergeometric function. Mathematical and Computer Modelling 2004,39(1):21–34. 10.1016/S0895-7177(04)90503-1
Carlson BC, Shaffer DB: Starlike and prestarlike hypergeometric functions. SIAM Journal on Mathematical Analysis 1984,15(4):737–745. 10.1137/0515057
Hohlov YuE: Operators and operations in the class of univalent functions. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika 1978, 10: 83–89.
Ruscheweyh S: New criteria for univalent functions. Proceedings of the American Mathematical Society 1975, 49: 109–115. 10.1090/S0002-9939-1975-0367176-1
Goel RM, Sohi NS: A new criterion for-valent functions. Proceedings of the American Mathematical Society 1980,78(3):353–357.
Owa S, Srivastava HM: Some applications of the generalized Libera integral operator. Proceedings of the Japan Academy, Series A 1986,62(4):125–128.
Liu J-L: The Noor integral and strongly starlike functions. Journal of Mathematical Analysis and Applications 2001,261(2):441–447. 10.1006/jmaa.2001.7489
Noor KI: On new classes of integral operators. Journal of Natural Geometry 1999,16(1–2):71–80.
Noor KI, Noor MA: On integral operators. Journal of Mathematical Analysis and Applications 1999,238(2):341–352. 10.1006/jmaa.1999.6501
Eenigenburg P, Miller SS, Mocanu PT, Reade MO: On a Briot-Bouquet differential subordination. In General Inequalities, 3 (Oberwolfach, 1981), Internationale Schriftenreihe zur Numerischen Mathematik. Volume 64. Birkhäuser, Basel, Switzerland; 1983:339–348.
Miller SS, Mocanu PT: Differential subordinations and univalent functions. The Michigan Mathematical Journal 1981,28(2):157–172.
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Kwon, O.S., Cho, N.E. Inclusion Properties for Certain Subclasses of Analytic Functions Associated with the Dziok-Srivastava Operator. J Inequal Appl 2007, 051079 (2007). https://doi.org/10.1155/2007/51079
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DOI: https://doi.org/10.1155/2007/51079