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Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions*

Published online by Cambridge University Press:  22 January 2016

H. M. Srivastava  and
Shigeyoshi Owa
H. M. Srivastava
Affiliation:
Department of Mathematics, University of Victoria, Victoria, British Columbia V8W 2Y2, Canada
Shigeyoshi Owa
Affiliation:
Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577, Japan
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By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disk are introduced and studied systematically. The various results presented here include, for example, a number of coefficient estimates and distortion theorems for functions belonging to these subclasses, some interesting relationships between these subclasses, and a wide variety of characterization theorems involving a certain functional, some general functions of hypergeometric type, and operators of fractional calculus. Some of the coefficient estimates obtained here are fruitfully applied in the investigation of certain subclasses of analytic functions with fixed finitely many coefficients.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 106 , June 1987 , pp. 1 - 28
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

Footnotes

*

The present investigation was carried out at the University of Victoria while the second author was on study leave from Kinki University, Osaka, Japan.

This work was supported, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant A-7353.

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