On the characterization of compactness in the space of functions of bounded variation in the sense of Jordan

2019/12/05 by Dariusz Bugajewski, Jacek Gulgowski
Engineering · Mathematics · #Stability and Controllability of Differential Equations #Nonlinear Differential Equations Analysis #Fixed Point Theorems Analysis

paper · doi:10.1016/j.jmaa.2019.123752

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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