Fixed Point and Interpolation Point Set of a Positive Linear Operator on C(d)
نویسنده
چکیده
Let D ⊂ R be a compact convex subset with nonempty interior. If A : C(D)→ C(D) is a positive linear operator with Π0(D) ⊂ FA or Π1(D) ⊂ FA then we establish some relations between the mixed-extremal point set of D and the interpolation point set of A. Our results include some well known results (see I. Raşa, Positive linear operators preserving linear functions, Ann. T. Popoviciu Seminar of Funct. Eq. Approx. Conv., 7(2009), 105-109) and the proofs are directly and elementarely.
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تاریخ انتشار 2010