Displaying similar documents to “On the range of a closed operator in an L 1 -space of vector-valued functions”

On quadratically integrable solutions of the second order linear equation

T. Chantladze, Nodar Kandelaki, Alexander Lomtatidze (2001)

Archivum Mathematicum

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Integral criteria are established for dim V i ( p ) = 0 and dim V i ( p ) = 1 , i ∈ { 0 , 1 } , where V i ( p ) is the space of solutions u of the equation u ' ' + p ( t ) u = 0 satisfying the condition ∫ + ∞ u 2 ( s ) s i d s < + ∞ .

The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems

Cristinel Mortici (2006)

Czechoslovak Mathematical Journal

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Let T be a γ -contraction on a Banach space Y and let S be an almost γ -contraction, i.e. sum of an ε , γ -contraction with a continuous, bounded function which is less than ε in norm. According to the contraction principle, there is a unique element u in Y for which u = T u . If moreover there exists v in Y with v = S v , then we will give estimates for ∥ u - v ∥ . Finally, we establish some inequalities related to the Cauchy problem.