African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 227

Full Length Research Paper

Applications of Cauchy-Schwarz inequalities in the mapping structure of linear operator

T. Panigrahi
  • T. Panigrahi
  • Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar-751024, Odisha, India.
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R. El-Ashwah
  • R. El-Ashwah
  • Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt.
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  •  Received: 06 November 2016
  •  Accepted: 22 February 2017
  •  Published: 30 June 2018

Abstract

By applications of Cauchy-Schwarz inequalities, several sufficient conditions in terms of hypergeometric inequalities were found such that the linear operator   preserves and transforms certain well known subclasses of univalent functions to another classes. Relevant connections of our work with the earlier work is pointed out.

Key words: Analytic function, subordination, starlike function, convex function, hypergeometric function, Cauchy-Schwarz inequality.