Displaying similar documents to “Central subsets of Urysohn universal spaces”

Functor of extension of Λ -isometric maps between central subsets of the unbounded Urysohn universal space

Piotr Niemiec (2010)

Commentationes Mathematicae Universitatis Carolinae

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The aim of the paper is to prove that in the unbounded Urysohn universal space 𝕌 there is a functor of extension of Λ -isometric maps (i.e. dilations) between central subsets of 𝕌 to Λ -isometric maps acting on the whole space. Special properties of the functor are established. It is also shown that the multiplicative group ℝ ∖ { 0 } acts continuously on 𝕌 by Λ -isometries.

Unique solvability of a linear problem with perturbed periodic boundary values

Bahman Mehri, Mohammad H. Nojumi (1999)

Czechoslovak Mathematical Journal

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We investigate the problem with perturbed periodic boundary values y ' ' ' ( x ) + a 2 ( x ) y ' ' ( x ) + a 1 ( x ) y ' ( x ) + a 0 ( x ) y ( x ) = f ( x ) , y ( i ) ( T ) = c y ( i ) ( 0 ) , i = 0 , 1 , 2 ; 0 < c < 1 with a 2 , a 1 , a 0 ∈ C [ 0 , T ] for some arbitrary positive real number T , by transforming the problem into an integral equation with the aid of a piecewise polynomial and utilizing the Fredholm alternative theorem to obtain a condition on the uniform norms of the coefficients a 2 , a 1 and a 0 which guarantees unique solvability of the problem. Besides having theoretical value, this problem has also important applications since decay is a phenomenon...