Fixed point sets for abstract volterra operators on Fréchet spaces

Dana M. Bedivan; Donal O′Regan

doi:10.1080/00036810008840871

Fixed point sets for abstract volterra operators on Fréchet spaces

Dana M. Bedivan
, Donal O′Regan

Mathematics

Alexandru Ioan Cuza University of Iasi

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

2 Citations (Scopus)

Abstract

In this present article the topological of the solution ser for abstract Volterra equations is studied both in Banach spaces and in Fréchet spaces. It is shown that the solution set for certain nonlinear abstract Volterra equations in the Fréchet spaces C[0,∞) and L ^p _loc [0,∞) (l≤p≤∞) are R _δ sets. Applications of the main results to nonlinear classical integral equations are given.

Original language	English
Pages (from-to)	131-152
Number of pages	22
Journal	Applicable Analysis
Volume	76
Issue number	1-2
DOIs	https://doi.org/10.1080/00036810008840871
Publication status	Published - Oct 2000

Keywords

47H15
47H30
Abstract Volterra operators
Equations in Fréchet spaces
Fixed points
Nonlinear integral equations

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10.1080/00036810008840871

Cite this

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abstract = " In this present article the topological of the solution ser for abstract Volterra equations is studied both in Banach spaces and in Fr{\'e}chet spaces. It is shown that the solution set for certain nonlinear abstract Volterra equations in the Fr{\'e}chet spaces C[0,∞) and L p loc [0,∞) (l≤p≤∞) are R δ sets. Applications of the main results to nonlinear classical integral equations are given.",

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AB - In this present article the topological of the solution ser for abstract Volterra equations is studied both in Banach spaces and in Fréchet spaces. It is shown that the solution set for certain nonlinear abstract Volterra equations in the Fréchet spaces C[0,∞) and L p loc [0,∞) (l≤p≤∞) are R δ sets. Applications of the main results to nonlinear classical integral equations are given.

KW - 47H15

KW - 47H30

KW - Abstract Volterra operators

KW - Equations in Fréchet spaces

KW - Fixed points

KW - Nonlinear integral equations

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Fixed point sets for abstract volterra operators on Fréchet spaces

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Keywords

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