The Jackson inequality and widths of function classes in L2([0,1],x2v+1)L2([0,1],x2v+1)

The sharp Jackson inequality between the best approximation of f∈L2([0,1],x2v+1)f∈L2([0,1],x2v+1) by a subspace LnLn—which is the linear hull of a finite orthogonal system of the functions constructed by the Bessel function of order vv of the first kind and its zeros—of L2([0,1],x2v+1)L2([0,1],x2v+1) and the generalized continuous modulus of order α>0α>0 of the generalized derivative of ff defined by a multiplier for some case with t>0t>0 is established. Moreover, the exact values of the nn-widths of the function classes S(α,λ,Ψ)S(α,λ,Ψ) and S(α,λ)S(α,λ) in the space L2([0,1],x2v+1)L2([0,1],x2v+1) are obtained.