Approximation theory has a significant place in the studies in mathematics, and the researches on it are increasing with each passing day. Accordingly, a number of studies have been presented about Bernstein approximation which is one of the most known linear positive operators. In this study, a new modification of Bernstein operators which fix constant and preserve Korovkin’s other test functions in limit case has been introduced. Then, the approximation properties of the newly defined operators such as asymptotic formulas, weighted approximation and rate of convergence have been presented. Moreover, numerical simulations are included. Finally, discussion and conclusions are presented.

中文翻译：

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关于伯恩斯坦算子的新修饰：理论与应用

逼近理论在数学研究中占有重要地位，并且它的研究日新月异。因此，已经提出了许多关于伯恩斯坦近似的研究，伯恩斯坦近似是最著名的线性正算子之一。在这项研究中，引入了Bernstein算子的新修改形式，该算子在常数情况下固定常数并保留Korovkin的其他测试函数。然后，给出了新定义算子的渐近性质，例如渐近公式，加权逼近和收敛速度。此外，还包括数值模拟。最后，给出了讨论和结论。