Voronovskaja’s Theorem in Terms of Weighted Modulus of Continuity

Let E be a subspace of C[0, ∞) which contains the polynomials and L n : E → C[0, ∞) be a sequence of linear positive operators. The weighted modulus of continuity, considered by Acar–Aral–Rasa in [7] is denoted by \(\Omega (f;\delta )\) and given by $$\displaystyle{\Omega (f;\delta ) =\sup _{0\leq h<\delta,x\in [0,\infty )}\frac{\vert f(x + h) - f(x)\vert } {(1 + h^{2})(1 + x^{2})} }$$