Approximation By Nonlinear Fourier Basis in Generalized Hölder Spaces
1Firat University, Department of Mathematics, ELAZIG
2Balikesir University, Department of Mathematics, BALIKESIR
2Balikesir University, Department of Mathematics, BALIKESIR
Sigma J Eng Nat Sci 2019; 10(): 135-142
Abstract
In this paper, the value of deviation of a function 𝑓 from its 𝑛th generalized de la Vallèe-Poussin mean 𝑉𝑛𝑎(𝜆,𝑓) with respect to the nonlinear trigonometric system is estimated for the classes of 2𝜋-periodic functions in the uniform norm ‖.‖𝐶(𝕋) and in the generalized Hölder norm ‖.‖𝜔𝛽 where 𝑓 ∈𝐻𝜔𝛼(𝕋) and 0≤𝛽<𝛼≤1.
Keywords: Generalized de la Vallèe-Poussin means, generalized Hölder class, nonlinear Fourier basis.
