The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.
This paper is concerned with a generalization in q-Calculus of Stancu operators. Involving modulus of continuity and Lipschitz type maximal function, we give estimates for the rate of convergence. A probabilistic approach is presented and approximation properties are established.
In this paper we obtain various approximation theorems by means of k-positive linear operators defined on the space of all analytic functions on a bounded domain of the complex plane.
In this paper we extend the Duman-King idea of approximation of functions by positive linear operators preserving , . Using a modification of certain operators preserving and , we introduce operators which preserve and and next we define operators for -times differentiable functions. We show that and have better approximation properties than and .
We introduce a sequence of positive linear operators including many integral type generalizations of well known operators. Using the concept of statistical convergence we obtain some Korovkin type approximation theorems for those operators, and compute the rates of statistical convergence. Furthermore, we deal with the local approximation and the rth order generalization of our operators.
It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space does not hold in all this space and is satisfied only on some subspace.