Bernstein-type Operators on a Triangle with One Curved Side

Interpolation Operators on Some Triangles with Curved Sides

“…Since the Bernstein-type operators interpolate a given function at the endpoints of the interval, these operators can also be used as interpolation operators both on triangles with straight sides (see, e.g., [9], [33], [34]) and with curved sides.…”

“…The aim of this survey is to present some interpolation and Bernsteintype operators for functions defined on triangles with one or all curved sides (see [11], [12], [14], [15]). They come as an extension of the corresponding operators for functions defined on triangles with all straight sides (see, e.g., [3]- [6], [8]- [10], [13], [23], [24], [26]- [29], [32]).…”

“…They come as an extension of the corresponding operators for functions defined on triangles with all straight sides (see, e.g., [3]- [6], [8]- [10], [13], [23], [24], [26]- [29], [32]). The operators defined on domains with curved sides permit essential boundary conditions to be satisfied exactly.…”

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

“…In order to match all the boundary information on a curved domain (as in Dirichlet, Neumann or Robin boundary conditions for differential equation problems), there were considered interpolation operators on domains with curved sides (see, e.g., [4], [6], [9]- [12], [15], [16], [20], [21], [23]). Approximation operators on polygonal domains with some curved sides have also important applications especially in finite element method for differential equations with given boundary conditions and in the piecewise generation of surfaces in computer aided geometric design.…”

Some Interpolation Operators on a Curved Domain

“…Such operators were considered in the papers [8], [7], [6]. Lately, such problems were studied in [2], [1], [3], [11], [9], [10], using interpolation operators.…”