Abstract

The main goal of this paper is to prove a compactness criterion for subsets of the Banach space of functions of bounded variation in the sense of Jordan. In comparison to the compactness criterion contained in Dunford–Schwartz's monograph, the conditions which appear in our criterion seems to be easier to verify. Moreover, using this criterion we define a quasimeasure of noncompactness in that space. Some applications of quasimeasures of noncompactness to fixed point theorems are also presented.

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