Some convergence results for nonlinear Baskakov-Durrmeyer operators - Altin, H.E. (Carpathian Mathematical Publications, 2023)
This paper is an introduction to a sequence of nonlinear Baskakov-Durrmeyer operators (NBD_n) of the form \[ (NBD_n)(f;x) =_0^∞ K_n(x,t,f(t)) dt \] with x[0,∞) and nN. While K_n(x,t,u) provide convenient assumptions, these operators work on bounded functions, which are defined on all finite subintervals of [0,∞). This paper comprise some pointwise convergence results for these operators in certain functional spaces. As well as this study can be seen as a continuation of studies about nonlinear operators, it is the first study on nonlinear Baskakov-Durrmeyer or modified Baskakov operators, while there were more papers on linear part of the operators.