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Approximation of functions by a new type of Gamma operators
(Wiley, 2020) Betus, Omur; Usta, Fuat
In this article, a new type of Gamma operators which preserves 1 and x(2) has been presented and tested. In order to show the approximation properties of the newly defined operator, Voronovksya type theorems, weighted approximation, rate of convergence, and pointwise estimates have been presented. Additionally, numerical examples implemented by MATLAB have been provided to show its approximation properties by numerically.
A new modification of Gamma operators with a better error estimation
(Taylor & Francis Ltd, 2020) Usta, Fuat; Betus, Omur
The present paper deals with new modification of Gamma operators preserving polynomials in Bohman-Korovkin sense and study their approximation properties: Voronovskaya type theorems, weighted approximation and rate of convergence are captured. The effectiveness of the newly modified operators according to classical ones are presented in certain senses as well. Numerical examples are also presented, highlighting the performance of the new constructions of Gamma operators in the context of one dimensional approximation.