Bojanov–Naidenov problem for differentiable functions and the Erdös problem for polynomials and splines
UDC 517.5 We solve the extremal problem \|x^(k)_±\|_L_p[a, b] → , k=0,1,… ,r-1,p > 0 , in the class of pairs (x, I) of functions xS^k_φ such that φ^(i) are the comparison functions for x^(i), i=0, 1,… ,k, and the intervals I = [a,b] satisfy the conditions L(x)_p A,μ {supp_[a, b] x^(k)_±\