Convergence of Approximation Processes on Convex Cones

M.S.M. Roversi, A.O. Chiacchio and M.L.B. Queiroz

Abstract: The purpose of this paper is to establish convergence results for sequences of convex conic operators on $C(X;\calc{C})$ which are regular, i.e., sequences $\{T_{n}\}_{n\ge1}$ such that for some positive linear operator $S_{n}$ on $C(X;\R)$ we have $T_{n}(g\otimes K)= S_{n}(g)\otimes K$, for every continuous real valued function $g$ and every element $K$ of the convex cone $\calc{C}$.

Keywords: Convex cone; regular operators; approximation.

Classification (MSC2000): 41A36, 41A65

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