Abstract

The class of functions of $\Lambda BV^{(p)}$ shares many properties of functions of bounded variation. Here we have shown that $\Lambda BV^{(p)}$ is a Banach space with a suitable norm, the intersection of $\Lambda BV^{(p)}$, over all sequences $\Lambda$, is the class of functions of BV$^{(p)}$ and the union of $\Lambda BV^{(p)}$, over all sequences $\Lambda$, is the class of functions having right- and left-hand limits at every point.

Keywords: Banach space, right and left-hand limits, p-$\Lambda$-bounded variation.

MSC: 26A45

Pages:  91$-$96     

Volume  58 ,  Issue  3$-$4 ,  2006