2022/03/23 by SERGEI SITNIK, S. M. Sitnik, Sitnik, S. M.
Mathematics · #26D15 #Differential Equations and Boundary Problems #FOS: Mathematics #History and Overview (math.HO) #Mathematical Inequalities and Applications #Mathematical functions and polynomials #math.HO #msc:26D15
paper · pdf · doi:10.48550/arxiv.2203.14344
39 pages. In Russian, English abstracts
arxiv created 2022/03/23 · openalex publication_date 2022/03/23 · arxiv updated 2022/03/29 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In this preprint we consider generalizations of discrete and integral Cauchy--Bunyakovskii inequalities by the method of mean values with some applications. Mostly the material is compiled as a short survey but some results are proved. Main results are listed, including an interesting inequality with maximum and minimum values. Some applications are considered from different fields of mathematics. Among them are estimates for some special functions, including Euler gamma and incomplete gamma function, the Legendre complete elliptic integrals of the first kind. Also some further possible generalizations are considered and outlined, including generalizations of the Aczél and Minkovskii inequalities, a case of spaces with sign-indefinite form, the Jackson's q-integrals.