Trigonometric approximation of signals (functions) belonging to certain Lipschitz spaces using C δ.C operator

Abstract

Abstract In 2015, Srivastava and Singh [S. K. Srivastava and U. Singh, Trigonometric approximation of periodic functions belonging to weighted Lipschitz class W ⁢ ( L p , Ψ ⁢ ( t ) , β ) W(L^{p},\Psi(t),\beta) , Function Spaces in Analysis, Contemp. Math. 645, American Mathematical Society, Providence 2015, 283–291] determined the order of approximation of periodic functions belonging to W ⁢ ( L p , Ψ ⁢ ( u ) , β ) {W(L^{p},\Psi(u),\beta)} -class, which is a weighted version of Lip ⁢ ( ω ⁢ ( u ) , p ) {\mathrm{Lip}(\omega(u),p)} -class with weight function sin β ⁢ p ⁡ ( y 2 ) {\sin^{\beta p}(\frac{y}{2})} through matrix means of their trigonometric Fourier series. It is a well-known fact that the product summability methods are stronger than the single summability methods, and they can approximate a wider class of functions. Therefore, in this article, an effort is made to determine the degree of approximation for periodic functions from the same weighted Lipschitz class W ⁢ ( L p , Ψ ⁢ ( u ) , β ) {W(L^{p},\Psi(u),\beta)} , p ≥ 1 {p\geq 1} , using C δ . T {C^{\delta}.T} -means of their trigonometric Fourier series.