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| 摘要: |
| 本文主要研究了修正的一元与二元Szasz-Mirakyan-Kantorovich算子的逼近问题.为此，首先证明了在加权Orlicz空间内的Korovkin型定理，在此基础上利用Jensen不等式，Hölder不等式，Steklov平均函数并结合相关分析技巧，获得了修正的一元与二元Szasz-Mirakyan-Kantorovich算子在加权Orlicz空间内的逼近正定理和收敛定理. |
| 关键词: Szasz-Mirakyan-Kantorovich算子 Orlicz空间 Korovkin型定理 逼近 |
| DOI： |
| 分类号:O174.41 |
| 基金项目:国家自然科学基金资助项目 (11761055);内蒙古师范大学基本科研业务费专项资金资助项目(2023JBZD007). |
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| WEIGHTED APPROXIMATION OF MODIFIED UNIVARIATE AND MULTIVARIATE SZASZ-MIRAKYAN-KANTOROVICH OPERATORS IN ORLICZ SPACES |
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CHEN Lin,WU Garidi
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| Abstract: |
| This article mainly studies the approximation problem of modified univariate and multivariate Szasz-Mirakyan-Kantorovich operators. In order to solve this problem, the Korovkin type theorem in weighted Orlicz spaces was first proved. Based on the Jensen inequality, Hölder inequality, Steklov mean function, and related analysis techniques, we obtained the approximation positive theorems and convergence theorems of the modified univariate and multivariate Szasz-Mirakyan-Kantorovich operators in weighted Orlicz spaces. |
| Key words: Szasz-Mirakyan-Kantorovich operators Orlicz space Korovkin type theorem approximation |
