Approximation of bounded variation functions by a Bézier variant of the Bleimann, Butzer, and Hahn operators.
In this paper we study the approximation of continuous functions F, defined on a compact Hausdorff space S, whose values F(t), for each t in S, are convex subsets of a normed space E. Both quantitative estimates (in the Hausdorff semimetric) and Bohman-Korovkin type approximation theorems for sequences of monotone operators are obtained.
We show the general and precise conditions on the functions and modulus of continuity as well as on the entries of matrices generating the summability means and give the rates of approximation of functions from the generalized integral Lipschitz classes by double matrix means of their Fourier series. Consequently, we give some results on norm approximation. Thus we essentially extend and improve our earlier results [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] and the result of S. Lal [Appl....
Let be harmonic in a bounded domain with smooth boundary. We prove that if the boundary values of belong to , where and denotes the surface measure of , then it is possible to approximate uniformly by function of bounded variation. An example is given that shows that this result does not extend to .