A generalized operator involving the $q$-hypergeometric function

Authors

  • Aabed Mohammed School of Mathematical Sceinces, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor D. Ehsan, Malaysia Author
  • Maslina Darus School of Mathematical Sceinces, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor D. Ehsan, Malaysia Author

Keywords:

$q$-hypergeometric functions, $q$-derivative, $q$-shifted factorial, general operator, integral means inequalities, neighborhood

Subjects:

30C45

Abstract

Motivated by the familiar $q$-hypergeometricfunctions, we introduce here a new general operator. By thisoperator, we define a subclass of analytic function. The classgeneralizes well known classes of starlike and convex functions.The integral means inequalities of this class are investigated.Also, we consider $p$-$\gamma$-neighborhood for functions in thisclass. Our result contains some interesting corollaries as itsspecial cases.

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Published

2013-10-15

Issue

Vol. 65 No. 4 (2013): Vol. 65, Issue 4

Section

Articles

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Copyright (c) 2013 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.