Extension of Some Positive and Linear Operators to Domains with Curved Sides

Abstract

Abstract. There are constructed some Cheney-Sharma type operators defined on a square with one curved side. They are extensions of the Cheney-Sharma type operators of second kind, given by E.W. Cheney and A. Sharma in [14], to the case of a curved sided domain. There are constructed the univariate Cheney-Sharma type operators, their product and boolean sum operators and there are studied their properties, their orders of accuracy and the remainders of the corresponding approximation formulas. Finally, there are given some illustrative examples.

Interpolation Operators on a Triangle With all Curved Sides

“…The aim of this survey is to present some interpolation and Cheney-Sharma type operators for functions defined on a triangle with all curved side (see [1], [2]). They came as an extension of the corresponding operators for functions defined on triangles with all straight sides (see, e.g., [3], [4], [9] ). We study these operators especially from the theoretical point of view.…”