Properties of a class of mean dependent on a parameter

• Published in: Journal of inequalities and applications Vol. 2019; no. 1; pp. 1 - 9
• Main Author: Bracken, Paul
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 17-07-2019; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Arithmetic; Bounded; Convergence; Mathematics; Mathematics and Statistics; Means; Parameters; Series; Series; 40A30; Means; Bounded; 33E20; Convergence; Arithmetic
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-019-2144-1

Some properties of a new class of binary symmetric mean
M
p
(
a
,
b
)
which depends on two positive numbers
a
and
b
, as well as a positive parameter
p
, are investigated. The logarithmic mean and arithmetic mean are two members of this class. It is shown that, for all values of the parameter
p
, the set of p-dependent means
M
p
(
a
,
b
)
is bounded above by the mean
M
∞
(
a
,
b
)
.