On The Lebesgue Function Of Generalized Freud-Type Weights And Two Kinds Of Interpolation Approximation

Interpolation theory is a mathematica thery.old but fashionable. Its abundant theories and advanced methods provide powerful and fruitful tools for solving approximation problems in the fields of science and technology.So more and more mathematicans are interested on it. It has become an active field in mathematics, We study three questions of them. According to the contents this paper is divided into four chapters.In the first chapter, we give the preface.In the second chapter, we generalize the result of the Lebesgue Function of Weighted Lagrange Interpolation of Freud-Type Weights to the result of the Lebesgue Function of generalized Freud-Type Weights, we concludeLet ω_rQ∈F, r is a nonnegative integer, ω > 0 is an arbitrary fixed number,then for any interpolation matrix X (?) [—a_n, a_n] without zero, there exist a constant c and setssuch thatif x ∈ [-a_n, a_n]\H_n,n ≥ n₁(ω).In the third chapter, we first conclude the existence, uniqueness and the characteristics of the best approximation paratrigonometric polynomials, then construct a kind of paratrigonometric Hermite interpolation for antiperiodic functions. We show that it is convergent for any antiperiodic continuous functions, we give a estimation of the convergence rate, thus we weakend the conditions requiring the analysis funtions when the convergence is studied in the paper[9]In the fourth chapter, we obtained a sharp estimation for the L_p convergence rate of the Grunwald interpolatory polynomials based on the zeros of Chebyshev polynomials of the firstkind...