On some inequalities for functions with nondecreasing increments of higher order

Journal of inequalities and applications

Asif R Khan¹ 

关键词: function with nondecreasing increments of higher order;    integral mean;    Levinson’s inequality;    monotonicity in means;   

DOI  :  10.1186/1029-242X-2013-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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 three, we obtain the Levinson-type inequality, a generalization of Burkill-Mirsky-Pečarić’s results, and a result for the integral mean of a function with nondecreasing increments of higher order.

【 授权许可】

CC BY