On the weighted Bojanov-Chebyshev problem and Fenton's sum of translates method

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Abstract

Minimax and maximin problems are investigated for a special class of functions on the interval [0,1]. These functions are sums of translates of positive multiples of one kernel function and a very general external field function. Due to our very general setting the minimax, equioscillation and characterization results obtained extend those of Bojanov, Fenton, Hardin, Kendall, Saff, Ambrus, Ball and Erdélyi. Moreover, we discover a surprising intertwining phenomenon of interval maxima, which provides new information even in the most classical extremal problem of Chebyshev.

About the authors

Bálint Farkas

University of Wuppertal

Author for correspondence.
Email: farkas@math.uni-wuppertal.de

Béla Nagy

Bolyai Institute, University of Szeged

Email: nbela@math.u-szeged.hu

Szilárd György Révész

Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences

Email: revesz.szilard@renyi.hu
Doctor of Science, Professor

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