Estimate on Logarithmic Co-Efficients of Sokol-Stankiewicz Type Star-Like Function Associated with Caratheodory Functions

The fundamental focus of researching coefficient problems for various families of univalent functions involves characterizing the coefficients of functions within a particular family based on the coefficients of Caratheodory functions. Consequently, by employing known inequalities for the class of Caratheodory functions, coefficient functionals can be scrutinized. This study will tackle several coefficient problems by applying the methodology to the aforementioned family of functions. Our investigation centers on the family of Sokol-Stankiewicz star-like functions which is defined in the open unit disk D. We explore the bounds of certain initial coefficients, including the Fekete-Szego inequality and other results concerning logarithmic coefficients for functions within this class.