Abstract

Using maximum instead of sum, nonlinear Favard-Szász-Mirakjan operator of maximum product kind was introduced. The present paper deals with the approximation processes for this operator. Especially in a previous study, it was indicated that the order of approximation of this operator to the function $f$ under the modulus is $\sqrt{x/n}$ and it could not be improved except for some subclasses of functions. Contrary to this claim, under some special conditions, we will show that a better order of approximation can be obtained with the help of classical and weighted modulus of continuities.

Keywords: Nonlinear Favard-Szász-Mirakjan operator; modulus of continuity; weighted modulus of continuity.

MSC: 41A36, 41A10, 41A25

DOI: 10.57016/MV-nkMX9624

Pages:  38--48     

Volume  77 ,  Issue  1 ,  2025