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On a problem concerning quasianalytic local rings

Hassan Sfouli (2014)

Annales Polonici Mathematici

Let (ₙ)ₙ be a quasianalytic differentiable system. Let m ∈ ℕ. We consider the following problem: let f ∈ m and f̂ be its Taylor series at 0 ∈ ℝ m . Split the set ℕ m of exponents into two disjoint subsets A and B, ℕ m = A ∪ B , and decompose the formal series f̂ into the sum of two formal series G and H, supported by A and B, respectively. Do there exist g , h ∈ m with Taylor series at zero G and H, respectively? The main result of this paper is the following: if we have a positive answer to the above problem for some m ≥ 2, then...

On almost everywhere differentiability of the metric projection on closed sets in l p ( ℝ n ) , 2 < p < ∞

Tord Sjödin (2018)

Czechoslovak Mathematical Journal

Let F be a closed subset of ℝ n and let P ( x ) denote the metric projection (closest point mapping) of x ∈ ℝ n onto F in l p -norm. A classical result of Asplund states that P is (Fréchet) differentiable almost everywhere (a.e.) in ℝ n in the Euclidean case p = 2 . We consider the case 2 < p < ∞ and prove that the i th component P i ( x ) of P ( x ) is differentiable a.e. if P i ( x ) ≠ x i and satisfies Hölder condition of order 1 / ( p - 1 ) if P i ( x ) = x i .

On an elementary inclusion problem and generalized weighted quasi-arithmetic means

Zoltán Daróczy, Zsolt Páles (2013)

Banach Center Publications

The aim of this note is to characterize the real coefficients p₁,...,pₙ and q₁,...,qₖ so that ∑ i = 1 n p i x i + ∑ j = 1 k q j y j ∈ c o n v x ₁ , . . . , x ₙ 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.

On an integral inequality.

Pečarić, J., Pejković, T. (2004)

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

On convex and *-concave multifunctions

Bożena Piątek (2005)

Annales Polonici Mathematici

A continuous multifunction F:[a,b] → clb(Y) is *-concave if and only if the inclusion 1 / ( t - s ) ∫ s t F ( x ) d x ⊂ ( F ( s ) * + F ( t ) ) / 2 holds for every s,t ∈ [a,b], s < t.

On derivo-periodic multifunctions

Libor Jüttner (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The problem of linearity of a multivalued derivative and consequently the problem of necessary and sufficient conditions for derivo-periodic multifunctions are investigated. The notion of a derivative of multivalued functions is understood in various ways. Advantages and disadvantages of these approaches are discussed.

Currently displaying 301 – 320 of 538