On Certain Analytic Functions Associated with Nephroid Function

The normalized analytic function ΦN(z)=1+z−z33, which connects the open unit disk onto a bounded domain within the right half of a nephroid-shaped region, is associated with the bounded turning of functions denoted by Rn. It calculates the sharp coefficient inequalities, which include the upper bound of the third Hankel determinant and Logarithmic coefficients related to the functions of the ΦN(z) class. This research mainly focuses on identifying solutions to specific coefficient-related problems for analytic functions within the domain of nephroid functions.