SZaSZ CHLODOWSKY TYPE OPERATORS COUPLING ADJOINT BERNOULLI'S POLYNOMIALS

This research work introduces a new connection of Sz<acute accent>asz operators with adjoint Bernoulli's polynomials as a new sequence of linear positive operators denoted by { S r,lambda ( .; .)}infinity 1. Further, convergence properties of these sequences of operators, i.e., { S r,lambda ( .; .)}infinity 1, are investigated in various functional spaces with the aid of the Korovkin theorem, a Voronovskaja type theorem, the first-order modulus of continuity, the second-order modulus of continuity, Peetre's K-functional, and the Lipschitz condition, etc. In the last section, we extend our research for the bivariate case of these sequences of operators, and their uniform rate of approximation and order of approximation are investigated in different functional spaces.