Abstract
In Chap. 3 the operator equations with continuous linear injective operator which acts in linear normed spaces are considered in greater detail. The spaces of strong and weak generalized solutions defined in previous chapter do not allow any constructive description in general case. In Sects. 3.1 and 3.2 we develop a variant of the theory, using the duality techniques, that is more useful for concrete applications. In Sects. 3.3 and 3.4 we study the alternative constructive approach to general solvability, based on the duality techniques.
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Klyushin, D.A., Lyashko, S.I., Nomirovskii, D.A., Petunin, Y.I., Semenov, V.V. (2012). A Priori Estimates for Linear Continuous Operators. In: Generalized Solutions of Operator Equations and Extreme Elements. Springer Optimization and Its Applications(), vol 55. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0619-8_3
Download citation
DOI: https://doi.org/10.1007/978-1-4614-0619-8_3
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-0618-1
Online ISBN: 978-1-4614-0619-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)