Rate of approximation for modified Lupaş-Jain-beta operators
Summary: The main intent of this paper is to innovate a new construction of modified Lupaş-Jain operators with weights of some Beta basis functions whose construction depends on \(\sigma\) such that \(\sigma(0)=0\) and \(\underset{x \in[ 0,\infty)}{\inf} \sigma^\prime(x)\geq1\). Primarily, for the sequence of operators, the convergence is discussed for functions belong to weighted spaces. Further, to prove pointwise convergence Voronovskaya type theorem is taken into consideration. Finally, quantitative estimates for the local approximation are discussed.
scientific article; zbMATH DE number 7385293
scientific article