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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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 332; no. 1; pp. 109 - 122
Main Authors: Patel, J., Mishra, A.K.
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.08.2007
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2006.09.067