In this paper, we study several important coefficient problems for the class of Sakaguchi‐type starlike functions subordinated to a petal‐shaped domain. We obtain a collection of sharp bounds that extend and refine known results in geometric function theory. Our main results include exact estimates for the first four logarithmic coefficients and the first five coefficients of the inverse functions. As applications, we resolve the classical Zalcman conjecture and certain generalized Krushkal‐type problems for this class by deriving sharp inequalities for functionals such as and . We also determine sharp second‐order Hankel determinants for both logarithmic and inverse coefficients, together with a strong bound for the third‐order Hankel determinant . The sharpness of all estimates is confirmed by identifying suitable extremal functions. Overall, the paper gives a unified and complete treatment of coefficient extremal problems for and provides optimal results that contribute to the theory of univalent functions. MSC2020 Classification: 30C45, 30C50, 30C80
Attiya et al. (Thu,) studied this question.