Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)*.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer Science+Business Media New York
About this chapter
Cite this chapter
Reinhardt, HJ. (1985). Compactness Criteria for Discrete Convergence. In: Analysis of Approximation Methods for Differential and Integral Equations. Applied Mathematical Sciences, vol 57. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1080-1_7
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1080-1_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96214-6
Online ISBN: 978-1-4612-1080-1
eBook Packages: Springer Book Archive