• Title, Summary, Keyword: approximate Henstock-Stieltjes integral

Search Result 1, Processing Time 0.02 seconds

A UNIFORM CONVERGENCE THEOREM FOR APPROXIMATE HENSTOCK-STIELTJES INTEGRAL

  • Im, Sung-Mo;Kim, Yung-Jinn;Rim, Dong-Il
    • Bulletin of the Korean Mathematical Society
    • /
    • v.41 no.2
    • /
    • pp.257-267
    • /
    • 2004
  • In this paper, we introduce, for each approximate distribution $\~{T}$ of [a, b], the approximate Henstock-Stieltjes integral with value in Banach spaces. The Henstock integral is a special case of this where $\~{T}\;=\;\{(\tau,\;[a,\;b])\;:\;{\tau}\;{\in}\;[a,\;b]\}$. This new concept generalizes Henstock integral and abstract Perron-Stieltjes integral. We establish a uniform convergence theorem for approximate Henstock-Stieltjes integral, which is an improvement of the uniform convergence theorem for Perron-Stieltjes integral by Schwabik [3].