| A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation |
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| 作者姓名： | 陈湛本 石济民 |
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| 作者单位： | Chen Zhanben (Guangzhou Institute of Systems Engineering，Guangzhou Teachers College) Shih Tsimin (Department of Applied Mathematics，The Hong Kong Polytechnic University) |
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| 摘 要： | §１． ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ１９０８，Ｅ．Ｌａｎｄａｕｉｎｔｒｏｄｕｃｅｄｔｈｅｆｏｌｌｏｗｉｎｇｗｅｌｌｋｎｏｗｎｓｅｑｕｅｎｃｅｏｆｏｐｅｒａｔｏｒｓ［１］Ｌｎ［ｆ（ｔ）；ｘ］＝Ｋｎ∫１－１ｆ（ｔ）［１－（ｔ－ｘ）２］ｎｄｔ， （１．１）ｗｈｅｒｅ Ｋｎ＝［∫１｛－１（１－ｔ２）ｎｄｔ］－１～ｎπ （ｎ→∞）．（１．１）ｗａｓｕｓｅｄｉｎｔｈｅｐｒｏｏｆｏｆｔｈｅＷｅｉｅｒｓｔｒａｓｓＴｈｅｏｒｅｍ．Ｓｉｎｃｅｔｈｅｎ，ｔｈｅａｐｐｒｏｘｉｍａｔｉｏｎｐｒｏｐ－ｅｒｔ…
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A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation |
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| Chen Zhanben.A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation[J].Chinese Quarterly Journal of Mathematics,1998(1). |
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| Authors: | Chen Zhanben |
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| Abstract: | In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 20, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n). |
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| Keywords: | generalized Landau linear positive operators degree of approximation asymptotic formula |
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