General Scheme of the Construction of Generalized Solutions of Operator Equations

D. A. Klyushin (), S. I. Lyashko (), D. A. Nomirovskii (), Yu. I. Petunin () and V. V. Semenov ()
Additional contact information
D. A. Klyushin: Kyiv National Taras Shevchenko University
S. I. Lyashko: Kyiv National Taras Shevchenko University
D. A. Nomirovskii: Kyiv National Taras Shevchenko University
Yu. I. Petunin: Kyiv National Taras Shevchenko University
V. V. Semenov: Kyiv National Taras Shevchenko University

Chapter Chapter 6 in Generalized Solutions of Operator Equations and Extreme Elements, 2012, pp 125-136 from Springer

Abstract: Abstract In Chap. 6 we propose the general approach to development of the theory of generalized solvability of linear operator equations. In Sect. 6.1 we prove the theorems on existence and uniqueness of generalized solutions of linear operator equations in locally convex linear spaces. In Sect. 6.2 we show that the proposed construction generalizes the definitions of generalized solutions given in Chaps. 2 and 3. We study the a priory inequalities method for proving theorems on existence of generalized solutions in abstract cases.

Keywords: Priori Inequalities; Minimal Cauchy Filter; Injective Continuous Linear Operator; Total Subset; Classical Solvability (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-0619-8_6

Ordering information: This item can be ordered from
http://www.springer.com/9781461406198

DOI: 10.1007/978-1-4614-0619-8_6

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().