MathDB
Problems
Contests
Undergraduate contests
Putnam
1972 Putnam
A3
A3
Part of
1972 Putnam
Problems
(1)
Putnam 1972 A3
Source: Putnam 1972
2/17/2022
A sequence
(
x
i
)
(x_{i})
(
x
i
)
is said to have a Cesaro limit exactly if
lim
n
→
∞
x
1
+
…
+
x
n
n
\lim_{n\to\infty} \frac{x_{1}+\ldots+x_{n}}{n}
lim
n
→
∞
n
x
1
+
…
+
x
n
exists. Find all real-valued functions
f
f
f
on the closed interval
[
0
,
1
]
[0, 1]
[
0
,
1
]
such that
(
f
(
x
i
)
)
(f(x_i))
(
f
(
x
i
))
has a Cesaro limit if and only if
(
x
i
)
(x_i)
(
x
i
)
has a Cesaro limit.
Putnam
Sequences
limit