engleski

On some inequalities for functions with nondecreasing increments of higher order

We investigate a class of functions with nondecreasing increments of higher order. A generalization of Brunk's theorem is proved for that class of functions. Also, we consider functions with nondecreasing increments of order 3, we obtain Levinson-type inequality, a generalization of Burkill-Mirsky-Pe\v cari\' c's results, and a result for the integral mean of a function with nondecreasing increments of higher order.

function with nondecreasing increments of higher order; integral mean; Levinson's inequality; monotonicity in means

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