Sharp generalized Seiffert mean bounds for the Toader mean of order 4

• Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 115; no. 3
• Main Authors: Li, Yanlin, Zhao, Tiehong
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-07-2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Original Paper; Theoretical; Toader mean; 26E60; Complete elliptic integral; Generalized Seiffert mean; 33E05
• ISSN: 1578-7303; 1579-1505
• DOI: 10.1007/s13398-021-01048-w

In the article, we present the best possible parameters
α
,
β
such that the double inequality
S
α
(
a
,
b
)
<
T
4
(
a
,
b
)
<
S
β
(
a
,
b
)
holds for
a
,
b
>
0
with
a
≠
b
, and provide new bounds for the complete elliptic integral of the second kind, where
S
p
(
a
,
b
)
and
T
4
(
a
,
b
)
are the generalized Seiffert mean and Toader mean of order 4, respectively.