Improving the order of approximation by a generalization of new bivariate sequence of integral type operators with parameters

Abstract

In this study, we define the bivariate new sequence of integral type operators which is denote by H_n(f(t, t); x, y) to approximation the functions in the spaces C_a ([0, ∞) × [0, ∞)), a > 0 and define a generalization of this sequence depends on a natural number S denote it by H_{n, s}(f; x, y) to get a better order of approximation by the sequence H_{n, s}(f; x, y). Firstly, we study some approximation properties for these sequences. Then, we discuss the simultaneous approximation for the r-th order partial derivatives for the sequence H_{n, s}(f; x, y). Also, we illustrate the order of approximation by Voronovskaja-type theorem. Finally, we demonstrate the convergence of the sequence H_{n, s}(f(t, t); x, y) to the function f by given some numerical examples and compare the numerical results obtained with the numerical results occurs from the sequence H_n(f; x, y).

Subject Classification:

• 41A25
• 41A28

Keywords:

• Voronovskaja theorem
• Order of approximation
• Bivariate modulus of continuity
• Simultaneous approximation