S-积分与Gronwall不等式(英文)

S-integral and Gronwall's Inequality

中文关键词:  S-积分  Gronwall-Bellman不等式

英文关键词:S-integral  Gronwall-Bellman's inequality

中文摘要:

      S-积分是利用Thomson的局部系定义的一种广义Riemann积分.本文证明了针对S-积分的Gronwall-Bellman不等式.作为特例,我们也获得了针对Henstock积分和Burkill近似连续积分的Gronwall-Bellman不等式.

英文摘要:

      The S-integral is a generalized integral of Riemann type which is defined in terms of the Thomson's local systems. In this note we prove Gronwall-Bellman's inequality for the S-integral. As special cases we also obtain Gronwall-Bellman's inequalities for the Henstock integral and the Burkill approximately continuous integral.