ON CONVERGENCE OF CERTAIN NONLINEAR DURRMEYER OPERATORS AT LEBESGUE POINTS

ABSTRACT. The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators NDnf of the form (NDnf)(x) = / Kn («,t, f (t)) dt, 0 < x < 1, NEN, acting on bounded functions on an interval [0, 1], where Kn (x, t, u) satisfies some suitable assumptions. Here we estimate the rate of convergence at a point , which is a Lebesgue point of f e Li ([0, 1) be such that Vof E BV ([0, 1]), where of denotes the composition of the functions U and f|. The function 4: RF → RT is continuous and concave with V(0) = 0, $(u) > 0 for u > 0, which appears from the (L- ) Lipschitz conditions.