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

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

Authors: Y. Polatoglu

Journal: Journal of Prime Research in Mathematics

HEC Recognition History
Category From To
Y 2023-07-01 2024-09-30
Y 2022-07-01 2023-06-30
Y 2021-07-01 2022-06-30
Y 2020-07-01 2021-06-30

Publisher: Abdus Salam School of Mathematical Sciences, GC University

Country: Pakistan

Year: 2010

Volume: 1

Issue: 1

Language: English

Keywords: λ− fractional Schwarzian derivativeλ− fractional Mobius transformation

Categories
Conformal Mapping (1) Mathematics (5170) Fractional Calculus (72) Complex Analysis (54) Differential Geometry (14)

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 \(\lambda\)− fractional Schwarzian derivative and \(\lambda\)− fractional Mobius transformation for the class A. We also formulate the criterion for a function to be univalent using the fractional Schwarzian.

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