Durrmeyer type operators on a simplex

Abstract

The paper contains the definition and certain approximation properties of a sequence of Durrmeyer type operators on a simplex, which preserve affine functions and make a link between the multidimensional "genuine" Durrmeyer operators and the multidimensional Bernstein operators.

Interpolation by Lupaş type operators on Tetrahedrons

“…For results related to Phillips and Lupaş type Bernstein operators on triangles, one can see recent work [10,11]. Approximation properties for Bernstein type polynomials and its remainder terms are evaluated by D. D Stancu in [30,31], R. Paltanea studied Durrmeyer type operators on a simplex in [16], A. Kajla and T. Acar studied blending type approximation by Bernstein durrmeyer type operators and α-Bernstein operators in [18,19].…”

A Note on Approximation of Blending Type Bernstein–Schurer–Kantorovich Operators with Shape Parameter α

“…Mohiuddine et al [6], Acu et al [7], İçöz and Çekim [8,9], and Kajla and Micláus [10,11] constructed new sequences of linear positive operators to investigate the rapidity of convergence and order of approximation in diferent functional spaces in terms of several generating functions. Some other researchers developed many other useful operators [6,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] in the same feld. In the recent past, for g ∈ [0, 1], m ∈ N and α ∈ [−1, 1], Chen et al [31] constructed a sequence of new linear positive operators as…”

A Modification of Bernstein-Durrmeyer Operators with Jacobi Weights on the Unit Interval

“…[14,12]); in particular, in [21] the author studied a generalization , , of Bernstein-Durrmeyer operators acting on weighted spaces of integrable functions, where the considered one is the classical Jacobi weight , on [0, 1]. Those operators have been intensely studied during the years in the one-dimensional and in multidimensional setting (see, e.g., [1,23,26]), also in connection with certain partial differential problems (see [5,7]).…”