The estimates of approximation by using a new type of weighted modulus of continuity

In this paper, we introduce a new type modulus of continuity for function ff belonging to a particular weighted subspace of C[0,∞)C[0,∞) and show that it has some properties of ordinary modulus of continuity. We obtain some estimates of approximation of functions with respect to a suitable weighted norm via the new type moduli of continuity. Finally, we give some examples.