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引用次数: 0
摘要
本文主要研究 Szász 算子的 Durrmeyer 型广义,包括汇合 Appell 多项式及其近似性质。同时,通过使用连续性模数和 Peetre 的 K 函数,我们发现了汇合 Durrmeyer 算子的收敛率。然后,我们证明了在 A(t) 的特殊选择下,新构造的算子分别还原了汇合赫米特多项式和汇合伯努利多项式。最后,我们将新构造的算子与 Durrmeyer 型 Szász 算子进行图解比较。
This article is concerned with the Durrmeyer-type generalization of Szász operators, including confluent Appell polynomials and their approximation properties. Also, the rate of convergence of the confluent Durrmeyer operators is found by using the modulus of continuity and Peetre’s K-functional. Then, we show that, under special choices of A(t), the newly constructed operators reduce confluent Hermite polynomials and confluent Bernoulli polynomials, respectively. Finally, we present a comparison of newly constructed operators with the Durrmeyer-type Szász operators graphically.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.