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In this study, we explore Toeplitz matrices composed of coefficients from new subclasses and establish upper limits for the initial four determinants like of these matrices. Our findings are innovative and unique, with the only similar results being in recent works by Thomas and Halim 1, which pertain to starlike and close - to - convex functions, and by Radhika et al. 2, focusing on functions with bounded boundary rotation. Along with we have determined the Zalcman, Generalized Zalcman conjecture and Krushkal inequalities for some parameters. Keywords: Star-like function, Convex function, Coefficient bounds, Univalent functions, Toeplitz matrices, Hankel determinants, Zalcman conjecture, Generalized Zalcman conjecture and Krushkal inequalities.
M. Nandeesh (Thu,) studied this question.