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Solvability of infinite systems of singular integral equations in Fréchet space of continuous functions

✍ Scribed by Leszek Olszowy

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
290 KB
Volume
59
Category
Article
ISSN
0898-1221

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✦ Synopsis

The aim of this paper is to show how some measures of noncompactness in the Fréchet space of continuous functions defined on an unbounded interval can be applied to an infinite system of singular integral equations. The results obtained generalize and improve several ones.

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Main Theorem: Let C be an infinite-dimensional convex set in a Fréchet space. If C has an almost internal point, then for every compact subset K of the completion Ten corollaries are derived from this theorem. Among them there are (1) conditions under which two convex sets with almost internal poin