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 Hn(f(t, t); x, y) to approximation the functions in the spaces Ca ([0, ∞) × [0, ∞)), a > 0 and define a generalization of this sequence depends on a natural number S denote it by Hn, s(f; x, y) to get a better order of approximation by the sequence Hn, 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 Hn, s(f; x, y). Also, we illustrate the order of approximation by Voronovskaja-type theorem. Finally, we demonstrate the convergence of the sequence Hn, 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 Hn(f; x, y).