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Some inequalities for the Čebyšev functional and general four-point quadrature formulae of Euler type

We use inequalities for the \v{; ; C}; ; eby\v{; ; s}; ; ev functional in terms of the first derivative (see \cite{; ; cerdrag}; ; ), for some new bounds for the remainder of four-point quadrature formulae of Euler type and its generalizations for Euler Bullen-Simpson's $3/8$ formula. As special cases, we consider some new bounds for Euler Simpson's $3/8$ formula, Euler Simpson's formula and Euler Gauss $2$-point formula.

\v{;; C};; eby\v{;; s};; ev functional; general four-point quadrature formulae of Euler type; Euler Bullen-Simpson's $3/8$ formula; Euler Simpson's $3/8$ formula; Euler Simpson's formula; Euler Gauss $2$-point formula.

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