Pointwise approximation by monotone sequences of polynomials (Q1276283)

The problem of the approximation of continuous functions on the interval \([-1,1]\) is widely investigated in the literature. \textit{S. G. Gal} and \textit{J. Szabados} obtained special monotone approximation polynomial sequences and gave uniform estimate [Acta Math. Hung. 59, No. 3/4, 395-399 (1992; Zbl 0766.41005)]. Later \textit{T. F. Xie} and \textit{S. P. Zhou} [Acta Math. Hung. 67, No. 1/2, 119-121 (1995; Zbl 0822.41008)] showed the possibility to construct such monotone polynomial sequences which do achieve the best uniform approximation rate. In this paper the author considers the pointwise estimate for such type of approximation and obtains a Jackson type rate.