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New subclasses of analytic functions defined by convolution involving the hypergeometric function and the Owa–Srivastava operator

  • Khalida Inayat Noor , Rashid Murtaza and Janusz Sokół ORCID logo EMAIL logo
Published/Copyright: March 13, 2018
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Abstract

In the present paper we introduce a new convolution operator on the class of all normalized analytic functions in |z|<1, by using the hypergeometric function and the Owa–Srivastava operator Ωα defined in [S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 1987, 5, 1057–1077]. This operator is a generalization of the operators defined in [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365] and [K. I. Noor, Integral operators defined by convolution with hypergeometric functions, Appl. Math. Comput. 182 2006, 2, 1872–1881]. Also we introduce some new subclasses of analytic functions using this operator and we discuss some interesting results, such as inclusion results and convolution properties. Our results generalize the results of [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365].

MSC 2010: 30C45; 30C10

Funding statement: This research is supported by the HEC NPRU project No: 20-1966/R&D/11-2553, titled “Research unit of Academic Excellence in Geometric Functions Theory and Applications”.

Acknowledgements

The authors are grateful to Dr. S. M. Junaid Zaidi, Rector, COMSATS Institute of Information Technology, Pakistan, for providing excellent research and academic environment. The authors would like to express their sincerest thanks to the referees for a careful reading and various suggestions made for the improvement of the paper.

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Received: 2015-08-18
Revised: 2016-07-17
Accepted: 2017-02-01
Published Online: 2018-03-13
Published in Print: 2019-09-01

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