Third Hankel Determinant and Zalcman Functional for Sakaguchi Type Starlike Functions Involving q-Derivative Operator Related with Sine Function

The purpose of this paper is to consider coefficient estimates for q-starlike function with respect to symmetric points associated with sine function \(SS^*_ q(1+sin(z))\) consisting of analytic functions \(f\) normalized by \(f(0)=f'(0)-1=0\) in the open unit disk \(U_d=\{ z:z∈ C and z <1\}\) satisfying the condition \(2[zD_qf(z)]/f(z)-f(-z){1+sin(z)}=ψ(z)\), for all \(z_d\) to derive certain coefficient estimates \(b_2,b_3\) etc and Fekete-Szeg\"{o} inequality for \(f^*_q(1+sin(z)).\) Further to investigate the possible upper bound of third order Hankel determinant and also the Zalcman functional for \(f^*_q(1+sin(z))\).