February, 2026

12-21

Erhan Deniz, Elif Aysegul Cin

In this paper, we introduce and investigate two Sakaguchi-type subclasses of normalized analytic functions which are generated by subordination to the Einstein function z E(z) = . ez − 1 The first class is defined through the Sakaguchi starlikeness expression, whereas the second one is obtained from the corresponding Sakaguchi convexity expression; accordingly, these classes are denoted by S∗ and C E , respectively. For functions f (z) = z + (cid:80)∞ n=2 a n zn belonging to these classes, we determine bounds fo E r the first three non-trivial Taylor coefficients and then use these coefficient relations to estimate the second-order Hankel determinants H 2,1 ( f ) and H 2,2 ( f ). We also obtain two-sided estimates for the Hermitian–Toeplitz determinants T 2,1 ( f ) and T 3,1 ( f ). The analysis is based on the Schwarz-function representation of subor- dination, coefficient comparison with the Einstein expansion, and the classical Carathe´odory coefficient parametrization, which enables the relevant determinant functionals to be reduced to explicitly tractable functions of two real parameters.

Deniz, E. & Cin, EA. (2026) Hankel and Hermitian–Toeplitz Determinants for Einstein-Type Sakaguchi Functions. Turkish Journal of Science. 11(1) 12-21.