An easily verifiable proof of the Brouwer fixed point theorem
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
math.HO↗
arXiv subjects
Tomonari Suzuki
Publications and source records attributed to Tomonari Suzuki.
The set of common fixed points of a one-parameter continuous semigroup of mappings is F(T(1)) cap F(T(sqrt 2))
In this paper, we prove the following theorem: Let {T(t) : t >= 0} be a one-parameter continuous semigroup of mappings on a subset C of a Banach space E. The set of fixed points of T(t) is denoted by F(T(t)) for each t >= 0. Then cap_{t >= 0} F(T(t)) = F(T(1)) cap F(T(sqrt 2)) holds. Using this theorem, we discuss convergence theorems to a common fixed point of {T(t) : t >= 0}.
math.FA↗
The set of common fixed points of an n-parameter continuous semigroup of mappings
In this paper, using Kronecker's theorem, we discuss the set of common fixed points of an n-parameter continuous semigroup of mappings. We also discuss convergence theorems to a common fixed point of an n-parameter nonexpansive semigroup.
math.FA↗
Fixed point theorems for asymptotically contractive mappings
In this short paper, we prove fixed point theorems for nonexpansive mappings whose domains are unbounded subsets of Banach spaces. These theorems are generalizations of Penot's result in [Proc. Amer. Math. Soc., 131 (2003), 2371--2377].
math.FA↗
An example for a one-parameter nonexpansive semigroup
We give one example for a one-parameter nonexpansive semigroup.
math.FA↗