Lupas-Baskakov型算子逼近的强逆不等式  

Strong converse inequalities on approximation of Lupas-Bakakov-Type operators

作　　者：马月梅[1] 刘国军[2] 

机构地区：[1]宁夏大学民族预科教育学院,银川750002 [2]宁夏大学数学计算机学院,银川750021

出　　处：《黑龙江大学自然科学学报》2014年第1期51-56,共6页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(61001156;61362029);宁夏自然科学基金资助项目(NZ1309);宁夏大学自然科学基金资助项目(ZR1232)

摘　　要：利用光滑模ωφ(f,t)和K-泛函K(f,t)之间的等价关系,讨论Lupas-Baskakov型算子在Lp[0,∞)(1≤p≤∞)空间的整体逼近。利用泰勒展开式、算子矩量估计、共鸣定理、Riesz插值定理、极大函数不等式、Cauchy-Schwarz不等式等分析技巧,得到了该算子逼近的强型逆向不等式。所得的结果类似于所对应的Baskakov和Szasz算子的结果。By using of the equivalent relationship between smooth modulus t% （f, t） and K-function- al K（f, t）, the global approximation by these operators is discussed in Lp[0,zz ） （ 1 〈p〈 ） spaces. Furthermore, the strong converse inequalities are obtained with some techniques of operator approxima- tion, such as Taylor＇ s expansion, moment estimation of operators, resonance theorem, Riesz interpolation theorem, maximum function inequality and Cauchy-Sehwarz inequality. The obtained results are similar to the corresponding ones of the Baskakov and Szasz operators.

关 键 词：关键词 Lupas BASKAKOV型算子 强逆不等式 逼近 光滑模 

分 类 号：O174.41[理学—数学]