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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we find the greatest values α, λ and the least values β, μ such that the double inequalities \(\alpha[G(a,b)/3+2A(a,b)/3]+(1-\alpha)G^{1/3}(a,b)A^{2/3}(a,b)< P(a,b) <\beta[G(a,b)/3+2A(a,b)/3]+(1-\beta)G^{1/3}(a,b)A^{2/3}(a,b)\) and \(\lambda [C(a,b)/3+2A(a,b)/3 ]+ (1-\lambda)C^{1/3}(a,b) A^{2/3}(a,b)< T(a,b)<\mu [C(a,b)/3+2A(a,b)/3 ]+(1-\mu)C^{1/3}(a,b) A^{2/3}(a,b)\) hold for all \(a,b>0\) with \(a\neq b\). Here \(G(a,b)\), \(A(a,b)\), \(C(a,b)\), \(P(a,b)\) and \(T(a,b)\) denote the geometric, arithmetic, contraharmonic, first Seiffert and second Seiffert means of two positive numbers a and b, respectively.

Optimal bounds for the first and second Seiffert means in terms of geometric, arithmetic and contraharmonic means