This paper aims to highlight a class of integral linear and positive operators of Landau type which have affine functions as fixed points. We focus to reveal approximation properties both in $$L_p$$ L p spaces and in weighted $$L_p$$ L p spaces $$(1\le p<\infty )$$ ( 1 ≤ p < ∞ ) . Also, we give an extension of the operators to approximate real-valued vector functions. In this case, the study pursues the approximation of continuous functions on convex compacts. The evaluation of the rate of convergence in one and multidimensional cases is performed by using adequate moduli of smoothness.

中文翻译：

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朗道类型算子对某些类函数的逼近

本文旨在重点介绍一类以仿射函数为不动点的Landau型积分线性正算子。我们专注于揭示 $$L_p$$ L p 空间和加权 $$L_p$$ L p 空间 $$(1\le p<\infty )$$ ( 1 ≤ p < ∞ ) 中的近似属性。此外，我们对运算符进行了扩展以逼近实值向量函数。在这种情况下，该研究追求凸压缩上连续函数的逼近。在一维和多维情况下的收敛速度的评估是通过使用足够的平滑模数来执行的。