Best Simultaneous L^p Approximation in the "Sum" Norm


In this paper we consider best simultaneous approximation byalgebraic polynomials respect to the norm \sum_{j=1}^k\|f_j-P\|_p, 1\le p<\infty. We prove an interpolation propertyof the best simultaneous approximations and we study the structureof the set of cluster points of the best simultaneousapproximations on the interval [-\epsilon,\epsilon], as \epsilon \to 0.

DOI Code: 10.1285/i15900932v28n2p153

Keywords: Simultaneous approximation; Algebraic polynomials; Lp-Norm

Classification: 41A28; 41A10

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