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A new class of nonexpansive type mappings and fixed points

Ljubomir B. Ćirić (1999)

Czechoslovak Mathematical Journal

In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.

A Non-standard Version of the Borsuk-Ulam Theorem

Carlos Biasi, Denise de Mattos (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

E. Pannwitz showed in 1952 that for any n ≥ 2, there exist continuous maps φ:Sⁿ→ Sⁿ and f:Sⁿ→ ℝ² such that f(x) ≠ f(φ(x)) for any x∈ Sⁿ. We prove that, under certain conditions, given continuous maps ψ,φ:X→ X and f:X→ ℝ², although the existence of a point x∈ X such that f(ψ(x)) = f(φ(x)) cannot always be assured, it is possible to establish an interesting relation between the points f(φ ψ(x)), f(φ²(x)) and f(ψ²(x)) when f(φ(x)) ≠ f(ψ(x)) for any x∈ X, and a non-standard version of the Borsuk-Ulam...

A note on asymptotic contractions.

Arav, Marina, Santos, Francisco Eduardo Castillo, Reich, Simeon, Zaslavski, Alexander J. (2007)

Fixed Point Theory and Applications [electronic only]

A note on f.p.p. and f * . p . p .

Hisao Kato (1993)

Colloquium Mathematicae

In [3], Kinoshita defined the notion of f * . p . p . and he proved that each compact AR has f * . p . p . In [4], Yonezawa gave some examples of not locally connected continua with f.p.p., but without f * . p . p . In general, for each n=1,2,..., there is an n-dimensional continuum X n with f.p.p., but without f * . p . p . such that X n is locally (n-2)-connected (see [4, Addendum]). In this note, we show that for each n-dimensional continuum X which is locally (n-1)-connected, X has f.p.p. if and only if X has f * . p . p .

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