engleski

Weighted Simpson’s inequalities and extension of Montgomery identity

Some new inequalities (error estimates) concerning weighted Simp- son type numerical integration for suitable function spaces and norms are proved, discussed and compared with similar results in the literature. As a natural preparation we also prove an extension of a weighted form of the Montgomery identity. As applications some new estimates for the expectation of a random variable X or, more generally a function of X, e.g. the r− moment Xr, are pointed out.

Lipschitz functions; functions of bounded variations; Lebesgue functions; mixed Lebesgue spaces; Simpson type formulas;

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