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    STUDIA MATHEMATICA - Issue no. 4 / 2010  
         
  Article:   FIXED POINT AND INTERPOLATION POINT SET OF A POSITIVE LINEAR OPERATOR ON C(D).

Authors:  IOAN A. RUS.
 
       
         
  Abstract:  Let be a compact convex subset with nonempty interior. If A : C(D) C(D) is a positive linear operator with or  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.

Key words and phrases. linear positive operator, fixed point set, interpolation point set, mixed-extremal point set.
 
         
     
         
         
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