On convergence rate for \(\varphi, \lambda\)-means of orthogonal series (Q1358585)

The author formulates four theorems pertaining to the approximation of orthogonal series \(\sum c_nf_n(x)\) by the very general \((\phi,\lambda,\gamma)\)-means. The summation methods \((\phi,\lambda,\gamma)\) include, among others, the following well-known methods: the Riesz method, the Cesàro methods \((C,\alpha)\), the Bernstein-Rogozinski method, the de la Vallée-Poussin methods and the Abel method. The author's theorems contain several known results proved by different authors for various concrete summation methods. The rate of approximation on these theorems depends on the coefficients \(\{c_n\}\).