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The least concave majorant, , of a continuous function on a closed interval, , is defined by
We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on . Given any function , it can be well-approximated on by a clamped cubic spline . We show that is then a good approximation to . We give two examples, one to illustrate, the other to apply our algorithm.
The main purpose of this paper is to give a new approach for partial metric spaces. We first provide the new concept of KM-fuzzy partial metric, as an extension of both the partial metric and KM-fuzzy metric. Then its relationship with the KM-fuzzy quasi-metric is established. In particularly, we construct a KM-fuzzy quasi-metric from a KM-fuzzy partial metric. Finally, after defining the notion of partial pseudo-metric systems, a one-to-one correspondence between partial pseudo-metric systems and...
We give a sufficient and necessary condition for a Radon-Nikodým compact space to be Eberlein compact in terms of a separable fibre connecting weak-* and norm approximation.
The purpose of this paper is to provide a new characterization of the Sobolev space . We also show a new proof of the characterization of the Sobolev space , 1 ≤ p < ∞, in terms of Poincaré inequalities.
2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10.
∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”,
Sofia, 2006.Certain types of weighted Peetre K-functionals are characterized by means
of the classical moduli of smoothness taken on a proper linear
transforms of the function. The weights with power-type asymptotic at the
ends of the interval with arbitrary real exponents are considered. This paper
extends the method and results presented...
A class of Banach spaces, countably determined in their weak topology (hence, WCD spaces) is defined and studied; we call them strongly weakly countably determined (SWCD) Banach spaces. The main results are the following: (i) A separable Banach space not containing ℓ¹(ℕ) is SWCD if and only if it has separable dual; thus in particular, not every separable Banach space is SWCD. (ii) If K is a compact space, then the space C(K) is SWCD if and only if K is countable.
In this paper we define and investigate a new subclass of those Banach spaces which are -analytic in their weak topology; we call them strongly weakly -analytic (SWKA) Banach spaces. The class of SWKA Banach spaces extends the known class of strongly weakly compactly generated (SWCG) Banach spaces (and their subspaces) and it is related to that in the same way as the familiar classes of weakly -analytic (WKA) and weakly compactly generated (WCG) Banach spaces are related. We show that: (i) not...
In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result...
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