Bulletin of the
Korean Mathematical Society BKMS

A class of normalized univalent functions $f$ defined in an open unit disk of the complex plane is introduced and studied such that the values of the quantity $zf'(z)/f(z)$ lies inside the evolute of a nephroid curve. The inclusion relations of the newly defined class with other subclasses of starlike functions and radius problems concerning the second partial sums are investigated. All the obtained results are sharp.

Keywords: Starlike functions, subordination, cusps, coefficient bound, partial sum, inclusion relations, nephroid, evolute

MSC numbers: 30C45, 30C50, 30C80