Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy
A discussion is given of some of the properties of the functional Volterra Integral equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy. and of the corresponding multidimensional equation. Sufficient conditions are given for the uniqueness of the solution, and an iterational process is provided for the constructio...
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000030 |
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| _version_ | 1849435053490176000 |
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| author | Li. G. Chambers |
| author_facet | Li. G. Chambers |
| author_sort | Li. G. Chambers |
| collection | DOAJ |
| description | A discussion is given of some of the properties of the functional
Volterra Integral equation
ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy.
and of the corresponding multidimensional equation. Sufficient conditions are
given for the uniqueness of the solution, and an iterational process is provided
for the construction of the solution, together with error estimates. In addition
bounds are provided on the solution. The results obtained are illustrated by
means of the pantograph equation. |
| format | Article |
| id | doaj-art-df5c7855759d4657906d0875b459757f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-df5c7855759d4657906d0875b459757f2025-08-20T03:26:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-01141274410.1155/S0161171291000030Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dyLi. G. Chambers0School of Mathematics, University College of North Wales, Gwynedd, Bangor LL57 1UT, UKA discussion is given of some of the properties of the functional Volterra Integral equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy. and of the corresponding multidimensional equation. Sufficient conditions are given for the uniqueness of the solution, and an iterational process is provided for the construction of the solution, together with error estimates. In addition bounds are provided on the solution. The results obtained are illustrated by means of the pantograph equation.http://dx.doi.org/10.1155/S0161171291000030functional integral equation. |
| spellingShingle | Li. G. Chambers Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy International Journal of Mathematics and Mathematical Sciences functional integral equation. |
| title | Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy |
| title_full | Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy |
| title_fullStr | Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy |
| title_full_unstemmed | Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy |
| title_short | Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy |
| title_sort | some properties of the functional equation ϕ x f x ∫0λxg x y ϕ y dy |
| topic | functional integral equation. |
| url | http://dx.doi.org/10.1155/S0161171291000030 |
| work_keys_str_mv | AT ligchambers somepropertiesofthefunctionalequationphxfx0lxgxyphydy |