Approximation of Integrable Functions by Modified Barbosu Operators

This paper presents an approximation method of integrable functions using a modified Barbosu operator, aimed at improving the rate of convergence in function approximation on the interval [0,1]. By introducing a suitable adjustment in the weight function, we construct a sequence of positive linear operators that better preserve the function's characteristics and demonstrate superior approximation behaviour, are studied. Theoretical error bounds are established in terms of the first and second order modulus of smoothness using their equivalence with the K-functionals. Finally, numerical experiments using test functions validate the theoretical findings and confirm that the King-type modified Barbosu operator achieve better approximation performance than the usual Kantorovich type Barbosu operator.