Glasnik Matematicki, Vol. 32, No.1 (1997), 57-69.

APPROXIMATION BY SOME OPERATORS OF THE SZASZ-MIRAKJAN TYPE IN EXPONENTIAL WEIGHT SPACES

M. Lesniewicz and L. Rempulska

Institute of Mathematics, Technical University of Poznan, Piotrowo 3 A, 60-965 Poznan, Poland


Abstract.   In this note we introduce some linear positive operators of the Szasz-Mirakjan type in the space of continuous functions of one and two variables, having exponential growth at infinity. In Sec. 1 we investigate the degree of approximation of functions of one variable by these operators. In Sec. 2 we give direct approximation theorems for functions of two variables.

This note was inspired M. Becker, D. Kucharski and R. J. Nessel results for the Szasz-Mirakjan operators.

1991 Mathematics Subject Classification.   41A36.

Key words and phrases.   Linear positive operators, degree of approximation.


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