Let E = [0, 1] and let a function p(x) > 1 be measurable and essentially bounded on E. We denote by L p(x) (E) the set of measurable function f on E for which R E |f(x)| p(x) dx < ∞. The convergence of a sequence of operators of Bernstein – Kantorovich {Kn(f, x)} ∞n=1 to the function f in Lebesgue spaces with variable exponent L p(x) (E) is studied.
