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    STUDIA MATHEMATICA - Ediţia nr.4 din 2010  
         
  Articol:   APPROXIMATION AND SHAPE PRESERVING PROPERTIES OF THE NONLINEAR BASKAKOV OPERATOR OF MAX-PRODUCT KIND.

Autori:  BARNABÁS BEDE. 		 
       
         
  Rezumat:  Starting from the study of the Shepard nonlinear operator of max-prod type in [2], [3], in the recent monograph [5], Open Problem 5.5.4, pp. 324-326, the Baskakov max-prod type operator is introduced and the question of the approximation order by this operator is raised. The aim of this note is to obtain for the discussed operator an upper pointwise estimate of the approximation error of the form (with the explicit constant C = 12) and to prove by a counterexample that in some sense, for arbitrary f this type of order of approximation with respect to ω1(f ;) cannot be improved. However, for some subclasses of functions including for example the nondecreasing concave functions, the essentially better order of approximation  is obtained. Finally, some shape preserving properties are proved.

Key words and phrases. Nonlinear Baskakov operator of max-product kind, degree of approximation, shape preserving properties. 		 
         
     
         
         
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