On certain subclasses of multivalent functions associated with an extended fractional differintegral operator

In the present paper an extended fractional differintegral operator Ω z ( λ , p ) ( − ∞ < λ < p + 1 ; p ∈ N ) , suitable for the study of multivalent functions is introduced. Various mapping properties and inclusion relationships between certain subclasses of multivalent functions are investig...

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Veröffentlicht in:	Journal of mathematical analysis and applications Jg. 332; H. 1; S. 109 - 122
Hauptverfasser:	Patel, J., Mishra, A.K.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	San Diego, CA Elsevier Inc 01.08.2007 Elsevier
Schlagworte:	Analytic function Differential subordination Exact sciences and technology Fractional differintegral operator Functions of a complex variable Gauss hypergeometric function Hadamard product (or convolution) Mathematical analysis Mathematics Multivalent function Sciences and techniques of general use Special functions Gauss hypergeometric function Analytic function Multivalent function Hadamard product (or convolution) Differential subordination Fractional differintegral operator Hadamard product Gauss function Convolution Mathematical analysis Hypergeometric function Application Analytical function
ISSN:	0022-247X, 1096-0813
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Abstract	In the present paper an extended fractional differintegral operator Ω z ( λ , p ) ( − ∞ < λ < p + 1 ; p ∈ N ) , suitable for the study of multivalent functions is introduced. Various mapping properties and inclusion relationships between certain subclasses of multivalent functions are investigated by applying the techniques of differential subordination. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.
AbstractList	In the present paper an extended fractional differintegral operator Ω z ( λ , p ) ( − ∞ < λ < p + 1 ; p ∈ N ) , suitable for the study of multivalent functions is introduced. Various mapping properties and inclusion relationships between certain subclasses of multivalent functions are investigated by applying the techniques of differential subordination. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out.
Author	Patel, J. Mishra, A.K.
Author_xml	– sequence: 1 givenname: J. surname: Patel fullname: Patel, J. email: jpatelmath@sify.com organization: Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar-751 004, Orissa, India – sequence: 2 givenname: A.K. surname: Mishra fullname: Mishra, A.K. email: akshayam2001@yahoo.co.in organization: Department of Mathematics, Berhampur University, Bhanja Bihar, Berhampur-760 007, Orissa, India
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Cites_doi	10.1016/S0022-247X(02)00500-0 10.1016/j.amc.2003.08.133 10.1016/j.aml.2004.09.003 10.4153/CJM-1987-054-3 10.1016/0022-0396(85)90082-8 10.1016/j.mcm.2003.06.010 10.1006/jmaa.1995.1342 10.1307/mmj/1029002507 10.1016/j.mcm.2005.06.014 10.1016/0022-247X(92)90373-L 10.1112/jlms/s2-9.4.530 10.1016/S0898-1221(00)00063-8 10.1090/S0002-9939-1975-0374403-3 10.1112/jlms/s2-21.2.287
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Keywords	Gauss hypergeometric function Analytic function Multivalent function Hadamard product (or convolution) Differential subordination Fractional differintegral operator Hadamard product Gauss function Convolution Mathematical analysis Hypergeometric function Application Analytical function
Language	English
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SubjectTerms	Analytic function Differential subordination Exact sciences and technology Fractional differintegral operator Functions of a complex variable Gauss hypergeometric function Hadamard product (or convolution) Mathematical analysis Mathematics Multivalent function Sciences and techniques of general use Special functions
Title	On certain subclasses of multivalent functions associated with an extended fractional differintegral operator
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