Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2750

Some properties of a generalized class of prestarlike functions

Muhammad Arif1, Khalida Inayat Noor2 and Janusz SokóÅ‚3
1Department of Mathematics, Abdul Wali Khan University Mardan, Pakistan. 2Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan. 3Department of Mathematics, Rzeszów University of Technology, ul. W. Pola 2, 35-959 Rzeszów, Poland.
Email: [email protected]

  •  Accepted: 30 March 2012
  •  Published: 19 November 2012

Abstract

In this article, we introduce the class of prestarlike functions of order  which generalizes the concept of prestarlike functions. We study here some interesting properties such as inclusion results, invariance under convolution and convex hull properties. Finally, a conjecture from our results which can be considered for future work is presented.

 

Key words: Convolution, test set, close-to-convex functions, Kaplan functions.