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In this note, we employ Jordan product within Banach algebras to present twoerror estimates of Lie-Trotter product formulas. Additionally, we introduce twogeneralized Lie-Trotter formula and provide two explicit estimation formulas.Consequently, the renowned Suzuki symmetrized approximation for theexponentiated sums follows directly from our Theorem 2.3. To conclude ourpaper, we offer a partial answer to a question concerning the Suzuki typeestimations in Jordan-Banach algebras.

Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in Banach Algebras