Establishes inequalities in approximating generalized Bernstein functions, indicating significant mathematical properties.
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a related function, namely xλΓ (x)/Γ (x+λ ) x λ Γ ( x ) / Γ ( x + λ ) are derived.
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Koumandos et al. (2026) studied this question.
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