Mursaleen M, Nasiruzzaman Md, Alotaibi Abdullah
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589 Saudi Arabia.
J Inequal Appl. 2017;2017(1):38. doi: 10.1186/s13660-017-1311-5. Epub 2017 Feb 7.
The purpose of this paper is to introduce a modification of -Dunkl generalization of exponential functions. These types of operators enable better error estimation on the interval [Formula: see text] than the classical ones. We obtain some approximation results via a well-known Korovkin-type theorem and a weighted Korovkin-type theorem. Further, we obtain the rate of convergence of the operators for functions belonging to the Lipschitz class.
本文的目的是介绍指数函数的 -邓克尔推广的一种修正。与经典算子相比，这类算子能在区间[公式：见原文]上实现更好的误差估计。我们通过一个著名的科罗夫金型定理和一个加权科罗夫金型定理得到了一些逼近结果。此外，我们还得到了属于利普希茨类函数的算子收敛速度。
