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On composition operator in the algebra of functions of two variables with bounded total Φ-variation in Schramm sense

Ereu T., Merentes N., Rzepka B., Sanchez J. L.

Journal of Mathematics and Applications

2010

Vol. 33

35-50

In this paper we consider the so called composition operator being a self-mapping of the Banach algebra of the function of two variables with bounded total Φ-variation in the Schramm sense. The main result of the paper characterizes the composition operator mentioned above which has a generating function being Lipschitzian with respect to the second variable. The basic tool used in our considerations is the concept of the left-left regularization.

Approximation of functions of two variables by modified Szasz-Mirakyan operators

Walczak Z.

Fasciculi Mathematici

2001

Nr 31

117-128

We consider certain modified Szasz-Mirakyan operators in the exponential weighted spaces of continuous functions of two variables. We prove theorems on the degree of approximation, the Voronovskaya type theorem and we study some differential properties of these operators. The similar results for functions of one variable were given in [1] and [2].

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].