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Symmetry 2018, 10(8), 348; https://doi.org/10.3390/sym10080348

Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes

1
Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea
2
Department of Mathematics, Ramanujan college, University of Delhi, H-Block, Kalkaji, New Delhi 110019, India
3
Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamil Nadu 620015, India
*
Author to whom correspondence should be addressed.
Received: 25 July 2018 / Revised: 10 August 2018 / Accepted: 14 August 2018 / Published: 18 August 2018
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
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Abstract

Higher order Schwarzian derivatives for normalized univalent functions were first considered by Schippers, and those of convex functions were considered by Dorff and Szynal. In the present investigation, higher order Schwarzian derivatives for the Janowski star-like and convex functions are considered, and sharp bounds for the first three consecutive derivatives are investigated. The results obtained in this paper generalize several existing results in this direction. View Full-Text
Keywords: higher order Schwarzian derivatives; Janowski star-like function; Janowski convex function; bound on derivatives higher order Schwarzian derivatives; Janowski star-like function; Janowski convex function; bound on derivatives
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. (CC BY 4.0).
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Cho, N.E.; Kumar, V.; Ravichandran, V. Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes. Symmetry 2018, 10, 348.

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