Construction of a New Family of Baskakov Operators Based on Negative λ-Binomial Distribution

We propose the λ-Baskakov operator based on λ-binomial distribution, which is a new Baskakov-type operator. First, the moments and the central moments for them and their quantitative properties are computed. Second, we obtain the rate of convergence of the new operators in different function spaces using the modulus of continuity, K-functional and Steklov mean function. Then, weighted approximation and point-wise estimates are also discussed. Finally, theoretical results are supported by illustrative graphics and tables using Matlab software.