C^p Condition and the Best Local Approximation  

作　　者：H.H.Cuenya D.E.Ferreyra 

机构地区：[1]Departamento de Matemática, Universidad Nacional de Río Cuarto

出　　处：《Analysis in Theory and Applications》2015年第1期58-67,共10页分析理论与应用（英文刊）

基　　金：supported by Universidad Nacional de Río Cuarto and Conicet

摘　　要：In this paper, we introduce a condition weaker than the LP differentiability, which we call Cp condition. We prove that if a function satisfies this condition at a point, then there exists the best local approximation at that point. We also give a necessary and sufficient condition for that a function be LP differentiable. In addition, we study the convexity of the set of cluster points of the net of best appoximations of f, {Pε（f）} asε→0.In this paper, we introduce a condition weaker than the LP differentiability, which we call Cp condition. We prove that if a function satisfies this condition at a point, then there exists the best local approximation at that point. We also give a necessary and sufficient condition for that a function be LP differentiable. In addition, we study the convexity of the set of cluster points of the net of best appoximations of f, {Pε（f）} asε→0.

关 键 词：Best L^p approximation local approximation L^p differentiability. 

分 类 号：O241.5[理学—计算数学]