The author studies the uniform convergence of extended Lagrange interpolation processes based on the zeros of Generalized Laguerre polynomials. 2009 Elsevier Inc. All rights reserved.

Uniform endpoint Lorentz norm improving estimates for convolution operators with affine arclength measure supported on simple plane curves are established. The estimates hold for a wide class of simple curves, and the condition is stated in terms of averages of the square of the affine arclength weight, extending previously known results. MSC: Primary 44A35; secondary 42B35

In this short paper, we summarize (without proofs) the constructive method to approximate functions in the uniform (i.e. maximal error) norm, that was recently developed by the authors. [9] This is in contrast to other methods (e.g. back-propagation) that approximate only in the average error norm. We comment on the novelty of the approach and possible extensions. The method includes a ~gradien...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.