Adjoint Bernoulli’s Kantorovich–Schurer-Type Operators: Univariate Approximations in Functional Spaces

Source abstract

In this work, we first establish a new connection between adjoint Bernoulli’s polynomials and gamma function as a new sequence of linear positive operators denoted by Sr,ς,λ(.;.). Further, convergence results for these sequences of operators, i.e., Sr,ς,λ(.;.) are derived in various functional spaces with the aid of the Korovkin theorem, the Voronovskaja-type theorem, the first order of the modulus of continuity, the second order of the modulus of continuity, Peetre’s K-functional, the Lipschitz condition, etc. In the last section, we focus our research on the bivariate extension of these sequences of operators; their uniform rate of approximation and order of approximation are investigated in different functional spaces.