Simultaneous Approximation By Generalization of Szãsz Type Operators
Abstract
In the present paper, we introduce a generalization of the Summation-Integral Szãsz type operators denoted by S ̃_(n,p) (f(t);x). First, we prove the convergence theorem for the operator. Then, we find a recurrence relation of the m-th order moment for the operator S ̃_(n,p) (f(t);x). Finally, we give a Voronovskaja-type asymptotic formula and an error estimate in terms of modulus of continuity of the function being approximate
Keywords
Linear positive operator, Simultaneous approximation, Voronovskaja-type asymptotic formula, Degree of approximation, Modulus of continuity. 2010 Mathematics Subject Classification. 41A36, 41A25.Metrics