Approximation with nonlinear Lototsky-Durrmeyer type operators

Abstract

The main objective of this study is to construct nonlinear Lototsky-Durrmeyer type operators and to investigate the approximation properties of these newly constructed operators. Research on Lototsky operators began with the work [Canad. J. Math. 1966, 18, 89-91] by J.P. King and approximation with nonlinear integral operators of convolution type was introduced by J. Musielak in 1983. In recent years, both theories have gained popularity through the work of many scientists. In this context, our primary motivation in this study is to introduce the nonlinear Lototsky-Durrmeyer type operators arising from the combination of these two theories and subsequently examine the approximation properties of these operators, particularly for functions with bounded variation and derivatives with bounded variation.