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Harmonic polynomials and generalizations of Ostrowski inequality

For a sequence $(P_{; ; ; k}; ; ; (t), k\geq 0)$ of polynomials satisfying the condition $$ P_{; ; ; k}; ; ; ^{; ; ; \prime }; ; ; (t)=P_{; ; ; k-1}; ; ; (t), \text{; ; ; }; ; ; k\geq 1 ; \text{; ; ; \ }; ; ; P_{; ; ; 0}; ; ; (t)=1, $$ we say that it is a harmonic sequence of polynomials. We give some generalizations of Ostrowski inequality, by using harmonic sequences of polynomials. We consider the Milovanovi\'{; ; ; c}; ; ; -Pe\v{; ; ; c}; ; ; ari\'{; ; ; c}; ; ; -Fink inequality, the Anastassiou's generalizations of the Ostrowski inequality and we give the generalizations of Ostrowski inequality via Euler harmonic identities.

function of bounded variation; harmonic polynomials; Lipschitz function; Ostrowski inequality

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