Geometric Nature of Special Functions on Domain Enclosed by Nephroid and Leminscate Curve

Autor: Reem Alzahrani, Saiful R. Mondal
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Symmetry, Vol 16, Iss 1, p 19 (2023)
Druh dokumentu: article
ISSN: 16010019
2073-8994
DOI: 10.3390/sym16010019
Popis: In this work, the geometric nature of solutions to two second-order differential equations, zy′′(z)+a(z)y′(z)+b(z)y(z)=0 and z2y′′(z)+a(z)y′(z)+b(z)y(z)=d(z), is studied. Here, a(z), b(z), and d(z) are analytic functions defined on the unit disc. Using differential subordination, we established that the normalized solution F(z) (with F(0) = 1) of above differential equations maps the unit disc to the domain bounded by the leminscate curve 1+z. We construct several examples by the judicious choice of a(z), b(z), and d(z). The examples include Bessel functions, Struve functions, the Bessel–Sturve kernel, confluent hypergeometric functions, and many other special functions. We also established a connection with the nephroid domain. Directly using subordination, we construct functions that are subordinated by a nephroid function. Two open problems are also suggested in the conclusion.
Databáze: Directory of Open Access Journals
Externí odkaz:
Nepřihlášeným uživatelům se plný text nezobrazuje