APPROXIMATION PROPERTIES OF JAIN-APPELL OPERATORS

Abstract

In this paper, we introduce the Jain-Appell operators by applying Gamma transform to the Jakimovski-Leviatan operators. In their special cases they include not only the Jain-Pethe operators, but also new families of operators, where we call them Appell-Baskakov and Appell-Lupas operators, since their special cases contain Baskakov and Lupas operators, respectively. We investigate their weighted approximation properties and compute the error of approximation by using certain Lipschitz class functions. Furthermore, we obtain their A-statistical approximation property.