Abstract: World Journal of Sensors Network Research

Abstract:
The paper is devoted to studying problems in the theory of approximation of periodic classes of functions by trigo nometric polynomials in the Hilbert space L2. Exact constants in Jackson-Stechkin type inequalities are obtained for functions , whose successive derivatives f(s) (s = 0,1,... ,r) belong to the space L2. Also, an exact value of simultaneous approximations of a function and its successive derivatives is obtained for certain classes of functions defined by the generalized modulus of continuity of higher orders Ωm (f(r),t)2 . For the class of functions Wm (r)(h), where m ∈N, r ∈Z+ , h ∈ (0,3π/(4n)], satisfying the constraint.