APPROXIMATION PROPERTIES OF MODIFIED GAUSS-WEIERSTRASS INTEGRAL OPERATORS IN EXPONENTIALLY WEIGHTED Lp SPACES

Abstract

In here, we use modi…ed Gauss-Weierstrass operators and givesome approximation results in the exponential weighted Lp spaces. Theseoperators are reproduce not only 1 but also a certain exponential functions.Forthis purpose, …rstly we consider modi…ed Gauss-Weierstrass integral operatorsfrom exponentially weighted Lp;a (R) into Lp;2a (R) spaces. Then, we give rate of convergence of the operators in Lp;2a (R) : Also, we prove the convergence of operators in the exponential weighted Lp;2a (R) spaces using the Korovkin type theorem. Finally, we give pointwise convergence of the operators at a generalized Lebesgue point.