Some Inequalities via Functional Type Generalization of Cauchy-Bunyakovsky- Schwarz Inequality - Inci Ege; Guldeniz Pasaoglu (Archives of Current Research International, 2025)
The Cauchy-Bunyakovsky-Schwarz inequality and its various refinements are very important in mathematical analysis. In this work, we first introduce an inequality of the form [f^(n)(x)]^2 ≤ k(x) _k=0^m a_k f^(m-k)(pr x+q) _k=0^l b_k f^(l-k)((2r-pr) x-q) and by using a functional type generalization of the Cauchy-Bunyakovsky-Schwarz inequality we get some inequalities for derivatives of a one-parameter deformation of the Gamma function to satisfy the introduced inequality. Also, we show that the established results are generalizations of some previous results.