A Generalization of Tyuriemskih's Lethargy Theorem and Some Applications

Tyuriemskih's Lethargy Theorem is generalized to provide a useful tool for establishing when a sequence of (not necessarily) linear operators that converges point wise to the identity operator actually converges arbitrarily slowly. Then this generalization is used to answer affirmatively a 2010 conjecture of ours as well as establishing that all of the classical operators of Bernstein, Hermite-Fejer, Landau, Fejer, and Jackson converge arbitrarily slowly to the identity operator (and not just almost arbitrarily slowly as we established in 2010).     

Iterative algorithms for generalized mixed equilibrium problems

In this paper, we consider a generalized mixed equilibrium problem in real Hilbert space. Using the auxiliary principle, we define a class of resolvent mappings. Further, using fixed point and resolvent methods, we give some iterative algorithms for solving generalized mixed equilibrium problem. Furthermore, we prove that the sequences generated by iterative algorithms converge weakly to the solution of generalized mixed equilibrium problem. These results require monotonicity (θ-pseudo monotonicity) and continuity (Lipschitz continuity) for mappings.     

复域中扰动Fejér点上Hermite——Fejér插值逼近的稳定性

该文在Jordan区域上研究扰动Fejér点上Hermite--Fejér插值对的逼近阶与收敛性, 完全解决了美国数学会 1991年Transactions of the AMS中Chui和Shen提出的问题,并将其边界条件J₂改进为.       

A NOTE ON THE WALSH-FEJER MEANS

The main aim of this paper is to prove that the maximal operator σ# is not bounded from the martingale Hardy space Hp （G） to the martingale Hardy space Hp （G） for 0〈p≤1.     

对Fejer积分的推广

利用对积分∫π0sinnx/sinx dx的递推解法,方便地得到Fejer积分的结果,并且对三次幂的情况进行推广.     

Fejer and Hermite-Hadamard type inequalities for superquadratic functions

In this paper we use basic properties of superquadratic functions to obtain new inequalities including Fejer's type and Hermite-Hadamard type inequalities. For superquadratic functions which are also convex, we get refinements of known results.     

Jacobi-Fourier级数的Fejer和对连续函数的逼近

研究了Jacobi-Fourier级数的Fejer和σα,βn(f)对连续函数f逼近的点态估计,改进了李中凯有关的结果.     

Pointwise convergence of cone-like restricted two-dimensional Fejér means of Walsh-Fourier series

For the two-dimensional Walsh system, Gat and Weisz proved the a.e. convergence of Fejer means σnf of integrable functions, where the set of indices is inside a positive cone around the identical function, that is, β^-1≤n1/n2 ≤β is provided with some fixed parameter ~ 〉 1. In this paper we generalize the result of Gat and Weisz. We not only generalize this theorem, but give a necessary and sufficient condition for cone-like sets in order to preserve this convergence property.