engleski

On a formula for the nth derivative and its application

In this paper we obtain a formula which involves the n th derivative of the first order divided difference and a corresponding inequality for functions whose (n + 1) -th derivative belongs to a Lp space. These results are a generalization of the results from [1] and [2]. Finally, some examples are given. ]1] T. H . GRO N WA L L, Problem 331., Amer. Math. Monthly, 20 (1913), 138. [2] T. H . GRO N WA L L, Problem 339., Amer. Math. Monthly, 20 (1913), 196

Holder inequality ; Lp spaces

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