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Rate of convergence for certain mixed family of linear positive operators

Maheshwari P., Sharma D.

Journal of Mathematics and Applications

2010

Vol. 33

73-78

The present paper deals with the mixed integrated operators Mn(f; x); which are linear and positive having different basis functions in summation and integration respectively. We estimate the rate of convergence for these operators for functions which have derivatives of bounded variation.

Direct and converse theorems for integral-type operators

Finta Z.

Demonstratio Mathematica

2003

Vol. 36, nr 1

137--147

We establish direct and converse results for integral-type operators defined with the aid of Szasz-Mirakjan operator and Baskakov operator, respectively. Moreover, some applications will be given.

Approximation theorems for some operators in weghted spaces of functions of two variables

Gurdek M., Kurczyńska J., Walczak Z.

Fasciculi Mathematici

1999

Nr 30

23-35

We study approximation properties of the Baskakov-Szasz-Mirakyan operators in some weighted spaces of functions of two variables. For these operators we give two theorems on the degree of approximation and the Voronovskaya type theorem. The Szasz-Mirakyan and Baskakov operators in the polynomial and exponential weighted spaces of functions of one variable were examined in [1]-[4]. Approximation theorems and the Voronovskaya type theorem for some operators ofthe Szasz-Mirakyan type were given in [5]-[7].