Compactness Criteria for Discrete Convergence

  • H.-J. Reinhardt
Part of the Applied Mathematical Sciences book series (AMS, volume 57)


We begin this chapter by defining the concept of a discretely compact sequence of elements, and use this notion to introduce the concepts of a-regular, regularly convergent, and discretely compact operator sequences. These properties provide criteria for inverse stability (respectively, bistability) which, as we know from the theory developed in the preceding chapter, are essential for deducing the inverse discrete convergence (respectively, biconvergence) of a sequence of mappings.


Compactness Criterion Discrete Approximation Uniform Boundedness Compactness Property Convergence Theory 
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  1. Anselone (1971), Anselone & Ansorge (1979,1981)*, Grigorieff (1972, 1973a,1975)*, Kato (1966), Krasnoselskii et al. (1972), Petryshyn (1968a, 1968b)*, Reinhardt (1975a)*, Stummel (1970,1973a,1976b)*, Vainikko (1969)*, Vainikko (1976), Wolf (1974)*.Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • H.-J. Reinhardt
    • 1
  1. 1.Fachbereich MathematikJohann-Wolfgang-Goethe-Universität6000 Frankfurt MainFederal Republic of Germany

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