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Displaying 141 –
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882
Let be a closed subset of and let denote the metric projection (closest point mapping) of onto in -norm. A classical result of Asplund states that is (Fréchet) differentiable almost everywhere (a.e.) in in the Euclidean case . We consider the case and prove that the th component of is differentiable a.e. if and satisfies Hölder condition of order if .
We investigate some properties of the normed space of almost periodic functions which are defined via the Denjoy-Perron (or equivalently, Henstock-Kurzweil) integral. In particular, we prove that this space is barrelled while it is not complete. We also prove that a linear differential equation with the non-homogenous term being an almost periodic function of such type, possesses a solution in the class under consideration.
The concept of almost quasicontinuity is investgated in this paper in several directions (e.g. the relation of this concept to other generalizations of continuity is described, various types of convergence of sequences of almost quasicontinuous function are studied, a.s.o.).
The aim of this note is to characterize the real coefficients p₁,...,pₙ and q₁,...,qₖ so that
be valid whenever the vectors x₁,...,xₙ, y₁,...,yₖ satisfy
y₁,...,yₖ ⊆ convx₁,...,xₙ.
Using this characterization, a class of generalized weighted quasi-arithmetic means is introduced and several open problems are formulated.
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