\(λ\)-fractional schwarzian derivative and \(λ\)-fractional mobius transformation

Y. Polatoglu
Department of Mathematics and Computer Science, Istanbul Kultur University, Bakırkoy 34156, Istanbul, Turkey.

\(^{1}\)Corresponding Author: y.polatoglu@iku.edu.tr

Copyright © 2010 Y. Polatoglu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2010.

Abstract

We denote by A the class of all analytic functions in the open unit disk \(\mathbb{D} = {z | |z| < 1}\) which satisfy the conditions \(f(0) = 0\), \(f'(0) = 1\). In this paper we define a new concept of \(λ\)− fractional Schwarzian derivative and \(λ\)− fractional Mobius transformation for the class A. We also formulate the criterion for a function to be univalent using the fractional Schwarzian.

Keywords:

\(λ\)-fractional integral, \(λ\)-fractional derivative.