Local Approximation by Modified Szász Operators

The concept of locally Hölder continuous functions with exponent α (0 < α ≤ 1) on a subset E subset of [0, ∞) is defined. This definition includes the concepts of globally Hölder continuous functions and of locally Hölder continuous functions at one point. Then the local approximation by modified Szász operators is considered. The locally Hölder continuous functions with exponent α (0 < α < 1) on any subset are characterized by the rate of local convergence of the modified Szász operators.