Optimal inequalities for bounding Toader mean by arithmetic and quadratic means

In this paper, we present the best possible parameters [Formula: see text] and [Formula: see text] such that the double inequality [Formula: see text] holds for all [Formula: see text] and [Formula: see text] with [Formula: see text] , and we provide new bounds for the complete elliptic integral [Fo...

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Detalles Bibliográficos
Autores principales: Zhao, Tie-Hong, Chu, Yu-Ming, Zhang, Wen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5266785/
https://www.ncbi.nlm.nih.gov/pubmed/28190939
http://dx.doi.org/10.1186/s13660-017-1300-8
Descripción
Sumario:In this paper, we present the best possible parameters [Formula: see text] and [Formula: see text] such that the double inequality [Formula: see text] holds for all [Formula: see text] and [Formula: see text] with [Formula: see text] , and we provide new bounds for the complete elliptic integral [Formula: see text] [Formula: see text] of the second kind, where [Formula: see text] , [Formula: see text] and [Formula: see text] are the Toader, arithmetic, and quadratic means of a and b, respectively.

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