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

On the weighted Bojanov-Chebyshev Problem and the sum of translates method of Fenton