English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this preprint we consider generalizations of discrete and integralCauchy--Bunyakovskii inequalities by the method of mean values with someapplications. Mostly the material is compiled as a short survey but someresults are proved. Main results are listed, including an interestinginequality with maximum and minimum values. Some applications are consideredfrom different fields of mathematics. Among them are estimates for some specialfunctions, including Euler gamma and incomplete gamma function, the Legendrecomplete elliptic integrals of the first kind. Also some further possiblegeneralizations are considered and outlined, including generalizations of theAcz\'el and Minkovskii inequalities, a case of spaces with sign-indefiniteform, the Jackson's $q$-integrals.

On generalizations of discrete and integral Cauchy-Bunyakovskii inequalities by the method of mean values. Some applications