Research On Some Approximation Problems In Orlicz Spaces

The function approximation theory is an important branch of modern mathematics,and it has a very brilliant role in many subjects.Compared with continuous function space and_pLspace,the topological structure of Orlicz space is more complex,and it is difficult to study approximation problems in Orlicz space.Therefore,it is of great significance and application prospect to discuss problems in Orlicz space.Based on previous works,we explore some generalized Baskakov linear operatorsapproximation,interpolation polynomial approximation,rational approximation and unilateral approximation problem of some functional classes in some Orlicz spaces,and get some meaningful results.This article is divided into five chapters.The first chapter introduces some basic knowledge about Orlicz space and unilateral approximation.The second chapter mainly studies the approximation theorem of two kinds of Baskakov linear operators in Orlicz space,which are divided into two sections:the first section mainly discusses the convergence of the two product Baskakov-Kantorovich operators on weighted Orlicz space,and then gives the operator approximation order estimation in Orlicz space;the second section,in continuous function spaces and spaces on the basis of the above approximation,we study the direct and inverse theorem of Szasz-Mirakjan-Baskakov operator in the Orlicz space approximation by using continuous mode,Holder inequality and Jensen inequality and so on.In the third chapter,we mainly study the approximation problem of rational interpolation in Orlicz space,which are divided into two section:the first section discusses two kinds of approximation Durrmeyer rational interpolation operator in Orlicz spaces with weight function;the second section discusses the approximation problem of Lagrange linear combination interpolation algorithm and Hermite interpolation operator in Orlicz space,and presents two kinds of estimation of approximation degree interpolation the result is more accurate,in previous similar results.In the fourth chapter,we mainly study the rational approximation in Orlicz space,which are divided into two sections:the first section,we study the Muntz rational function approximation problems in Orlicz spaces by using modified Bak operators,and present two kinds of estimation of approximation order smooth function Muntz rational,the result is better than before the similar results.the second section,we study the approximation problem of a kind rational function in Orlicz space.Under the condition that the approximation function changes l sub symbols,a Jackson type estimation of the approximation order is given with the help of the Steklov mean function.In the fifth chapter,unilateral approximation problem is studied.It is assumed that functions K?x?that periodic is 2?satisfy the properties B or NCVD kernel.In this section,we obtain the exact value of the convolution classes ???_M or ???_M of the one sided approximation of trigonometric polynomial and periodic spline under the L₁ scale.