By using two given arbitrary sequences alpha(n) > 0, beta(n) > 0, n is an element of N with the property that lim(n ->infinity) beta(n)/alpha(n) = 0, in this very short note we modify the generalized Szasz-Mirakjan operator based on the Sheffer polynomials in such a way that on each compact subinterval in 0,+ infinity) the order of uniform approximation is omega(1)(f; root beta(n)/alpha(n)). These modified generalized operators can uniformly approximate a Lipschitz 1 function, on each compact subinterval of 0, infinity) with an arbitrary good order of approximation root beta(n)/alpha(n).
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