Approximation of functions of space L 2(ℝ) by wavelet expansions

The approximations of a function belonging Hölder class Hα[0,1) by second kind Chebyshev wavelet method and applications in solutions of differential equation

“…Rehman et al 14 have solved the fractional differential equations by Legendre Wavelet methods. Lal et al 10 determined the approximation of functions belonging to L 2 [0, 1) space by Wavelet expansion. Hojatollah et al 1 have studied the approximation of functions by Chebyshev first kind Wavelet Method.…”

Quasi-Positive Delta Sequences and Their Applications in Wavelet Approximation

“…Some properties of wavelet expansions have been studied by Chui [1], Daubechies and Lagarias [2], Meyer [3], Walter [4,5], Islam et al [6], and so forth. The idea of approximation of various functional spaces under different norms is obtained by Lal and Kumar [7,8], Abu-Sirhan [9], Coskun [10], and Shiri and Azadi Kenary [11] which gives the inspiration for the present work. But till now no work seems to have been done to obtain the wavelet approximation of a function ∈ Lip [ , ], 0 < ≤ 1 using the projection ( ) of its wavelet expansion and to discuss its convergence.…”

Legendre Wavelet Expansion of a Function f(x, y) and its Approximation

“…Legendre wavelets possess the orthogonality property. Some results concerning to Legendre wavelet and Haar wavelet have been discussed by researchers Islam [3], Lal and Kumar [5], Lal and Kumar [6], Nanshan [4] and Razzaghi [2] etc. The Legendre wavelet approximation of functions of two variables have not been discussed so far.…”