ON CONVERGENCE OF CERTAIN NONLINEAR DURRMEYER OPERATORS AT LEBESGUE POINTS

The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators ND(n)f of the form (ND(n)f)(x) = integral K-1(0)n (x,t, f (t))dt, 0 <= x <= 1, n is an element of N, acting on bounded functions on an interval [0, 1], where K-n (x, t, u) satisfies some suitable assumptions. Here we estimate the rate of convergence at a point x, which is a Lebesgue point of f is an element of L-1 ([0,1]) be such that psi(o) vertical bar f vertical bar is an element of BV ([0, 1]), where psi(o) vertical bar f vertical bar denotes the composition of the functions psi and vertical bar f vertical bar. The function psi : R-0(+) -> R-0(+) is continuous and concave with psi(0) = 0, psi(u) > 0 for u > 0, which appears from the (L - psi) Lipschitz conditions.