2021/08/17 by Jitendra Kumar Singh, Purshottam Narain Agrawal, P. Ν. Agrawal +1
Mathematics · #Approximation Theory and Sequence Spaces #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials
paper · doi:10.1080/03081087.2021.1960260
In this article, we introduce a q-analogue of the operators defined by Usta and Betus (Linear Multilinear Algebra, DOI: 10.1080/03081087.2020.1791033 (2020)) and find a general expression of moments for the q- operators. Next, we study the approximation properties of these operators in a weighted space via A-statistical method and the power series method. Later, we define a k-th order generalization of the q- operators by using the approach of Kirov and Popova (Math. Balk. 7, 149–162 (1993)) and estimate the error in the approximation for the Ck functions in a Lipschitz class. We modify these operators so that they reproduce the constant as well as a monomial and provide better approximation. Finally, we introduce some graphical results to validate our theoretical claims.