Translator Disclaimer
november 2019 Geometric features of general differential solutions
Rosihan M. Ali, See Keong Lee, Saiful R. Mondal
Bull. Belg. Math. Soc. Simon Stevin 26(4): 551-570 (november 2019). DOI: 10.36045/bbms/1576206357

Abstract

This papers examines the general differential equation \[y''(z)+a(z) y'(z)+ b(z)y(z)=0\] in the unit disk of the complex plane, and finds conditions on the analytic functions $a$ and $b$ that ensures the solutions are Janowski starlike. Also studied is Janowski convexity of solutions to \[z (1-z)y''(z)+ a(z) y'(z)+ \alpha y(z) =0,\] where $\alpha$ is a given constant. Janowski starlikeness and Janowski convexity encompass various widely studied classes of classical starlikeness and convexity. As application, we give convexity and starlikeness geometric description of solutions to differential equations related to several important special functions.

Citation

Download Citation

Rosihan M. Ali. See Keong Lee. Saiful R. Mondal. "Geometric features of general differential solutions." Bull. Belg. Math. Soc. Simon Stevin 26 (4) 551 - 570, november 2019. https://doi.org/10.36045/bbms/1576206357

Information

Published: november 2019
First available in Project Euclid: 13 December 2019

zbMATH: 07167744
MathSciNet: MR4042401
Digital Object Identifier: 10.36045/bbms/1576206357

Subjects:
Primary: 30C45, 33C05, 34A30

Rights: Copyright © 2019 The Belgian Mathematical Society

JOURNAL ARTICLE
20 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.26 • No. 4 • november 2019
Back to Top