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In a quasi-gauge space ( X , P ) with quasi-gauge P , using the left (right) J -families of generalized quasi-pseudodistances on X ( J -families on X generalize quasi-gauge P ), the left (right) quasi-distances D η L − J ( D η R − J ) of Hausdorff type on 2 X are defined, η ∈ { 1 , 2 , 3 } , the three kinds of left (right) set-valued contractions...
Let X be a nonempty set of cardinality at most 2^[aleph]0 and T be a selfmap of X. Our main theorem says that if each periodic point of T is a fixed point under T, and T has a fixed point, then there exist a metric d on X and a lower semicontinuous map [phi] : X --> R+ such that d(x,Tx] is less than or equal phi[x] - phi(Tx) for all x belongs to X, and (X, d) is separable. Assuming CH (the Continuum...
We give some conditions under which commuting triangular maps have a common fixed point. Some of them provide analogons of known results for maps of a real interval.
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