Abstract
We present a realization for some K-functionals associated with Jacobi expansions in terms of generalized Jacobi–Weierstrass operators. Fractional powers of the operators as well as results concerning simultaneous approximation and Nikolskii–Stechkin type inequalities are also considered.
Highlights
1 Introduction In this note, we work with two fixed real parameters α and β satisfying α ≥ β ≥ –1/2
For each n ∈ N0, Pn is the family of all algebraic polynomials of degree not greater than n, wnα,β
It follows from Theorem 3.9 of [15] that the family of operators {Ct,γ : t > 0} is uniformly bounded
Summary
We work with two fixed real parameters α and β satisfying α ≥ β ≥ –1/2. Theorem 2.1 For each h ∈ [–1, 1), there exists a function τh : X → X with the following properties: (i) For each f ∈ X, one has τhf X ≤ f X , and lim τh(f ) – f h→1– It follows from Theorem 3.9 of [15] that the family of operators {Ct,γ : t > 0} is uniformly bounded.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
