Journal of Applied Sciences

Year: 2006 | Volume: 6 | Issue: 8 | Page No.: 1798-1801
DOI: 10.3923/jas.2006.1798.1801

Statistically Improved Approximation By Modified Lupas Operator

Ashok Sahai, Angela Shirley and M. Raghunadh Acharya

Abstract: In 1950, Szasz proposed a generalization of the well-known Bernstein’s polynomials extending it to the infinite interval. Many authors such as, Hermann in 1977, studied its use in the approximations of functions on an unbounded interval. The actual construction of the Szasz-Mirakjan Operator, say S_n(f;x), requires estimation per infinite series, which apparently restricts its practical usefulness from the computational point-of-view. In 1980, Grof introduced ‘Modified Szasz-Mirakjan Operator’ which was a finite ‘partial sum’ curtailment of S_n(f;x) and studied it. In 1984, Heinz-Gerd Lehnhoff, in particular, proposed for f and x ε C [0, 1] another ‘Modified Szasz-Mirakjan Operator’: S_n(f;x) = . We have proposed and studied a statistically motivated improvement of the Lupas Operator modified analogously. The study is supported and illustrated by the following empirical simulation study aimed at bringing forth the potential improvement numerically for some standard types of function.