APPLICATIONS OF CESÀRO SUBMETHOD TO APPROXIMATION OF FUNCTIONS IN WEIGHTED ORLICZ SPACES

In this work, the approximation properties of the matrix submethods in weighted Orlicz spaces with Muckenhoupt weights are studied. We obtain some results related to trigonometric approximation using matrix submethods of partial sums of Fourier series of functions in the weighted Orlicz spaces with Muckenhoupt weights.The degree of trigonometric approximations by the matrix methods to the functions have been investigated in weighted Orlicz spaces with Mucken-houpt weights. The error of estimations in this work is obtained in more general terms. In many studies the classical Cesàro method was used to obtain the estimations. In this study to obtain these estimations we use Cesàro submethod instead of classical Cesàro method. © 2023, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved