Starlike functions associated with an epicycloid

Authors : Shweta GANDHİ, Prachi GUPTA, Sumıt NAGPAL, V RAVİCHANDRAN

Pages : 1637-1660

Doi:10.15672/hujms.1019973

View : 17 | Download : 6

Publication Date : 2022-12-01

Article Type : Research Paper

Abstract :For a natural number $n\geq 2$, the function $\phi_{n\mathcal{L}}insert ignore into journalissuearticles values(z);=1+nz/insert ignore into journalissuearticles values(n+1);+z^n/insert ignore into journalissuearticles values(n+1);$ maps the open unit disk onto a domain bounded by an epicycloid with $insert ignore into journalissuearticles values(n-1);$ cusps. A class of starlike functions associated with $\phi_{n\mathcal{L}}$ is defined in the unit disk and its sharp bounds on initial coefficients, various inclusion relations and radii problems related to the other subclasses of starlike functions are investigated. As an application, the corresponding results are determined in the limiting case for the class of normalized analytic functions $f$ satisfying $|zf`insert ignore into journalissuearticles values(z);/finsert ignore into journalissuearticles values(z);-1|<1$ in the unit disk.
Keywords : radius problem, starlike functions, cusps, three leaf domain, inclusion relation, coefficient bound, epicycloid, subordination