Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in L p Spaces

Detalhes bibliográficos
Autor(a) principal: AFONSO,S. M.
Data de Publicação: 2019
Outros Autores: AZEVEDO,J. S., DA SILVA,M. P. G., ROCHA,A. M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512019000300403
Resumo: ABSTRACT In this work we consider the general functional-integral equation: y ( t ) = f ( t , ∫ 0 1 k ( t , s ) g ( s , y ( s ) ) d s ) , t ∈ [ 0 , 1 ] , and give conditions that guarantee existence and uniqueness of solution in L p ( [ 0 , 1 ] ), with 1 1 p ∞.We use Banach Fixed Point Theorem and employ the successive approximation method and Chebyshev quadrature for approximating the values of integrals. Finally, to illustrate the results of this work, we provide some numerical examples.
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spelling Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in L p Spacesfunctional-integral equationsLp spacesexistenceuniquenesssuccessive approximationABSTRACT In this work we consider the general functional-integral equation: y ( t ) = f ( t , ∫ 0 1 k ( t , s ) g ( s , y ( s ) ) d s ) , t ∈ [ 0 , 1 ] , and give conditions that guarantee existence and uniqueness of solution in L p ( [ 0 , 1 ] ), with 1 1 p ∞.We use Banach Fixed Point Theorem and employ the successive approximation method and Chebyshev quadrature for approximating the values of integrals. Finally, to illustrate the results of this work, we provide some numerical examples.Sociedade Brasileira de Matemática Aplicada e Computacional2019-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512019000300403TEMA (São Carlos) v.20 n.3 2019reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2019.020.03.0403info:eu-repo/semantics/openAccessAFONSO,S. M.AZEVEDO,J. S.DA SILVA,M. P. G.ROCHA,A. M.eng2019-12-12T00:00:00Zoai:scielo:S2179-84512019000300403Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2019-12-12T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in L p Spaces
title Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in L p Spaces
spellingShingle Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in L p Spaces
AFONSO,S. M.
functional-integral equations
Lp spaces
existence
uniqueness
successive approximation
title_short Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in L p Spaces
title_full Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in L p Spaces
title_fullStr Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in L p Spaces
title_full_unstemmed Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in L p Spaces
title_sort Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in L p Spaces
author AFONSO,S. M.
author_facet AFONSO,S. M.
AZEVEDO,J. S.
DA SILVA,M. P. G.
ROCHA,A. M.
author_role author
author2 AZEVEDO,J. S.
DA SILVA,M. P. G.
ROCHA,A. M.
author2_role author
author
author
dc.contributor.author.fl_str_mv AFONSO,S. M.
AZEVEDO,J. S.
DA SILVA,M. P. G.
ROCHA,A. M.
dc.subject.por.fl_str_mv functional-integral equations
Lp spaces
existence
uniqueness
successive approximation
topic functional-integral equations
Lp spaces
existence
uniqueness
successive approximation
description ABSTRACT In this work we consider the general functional-integral equation: y ( t ) = f ( t , ∫ 0 1 k ( t , s ) g ( s , y ( s ) ) d s ) , t ∈ [ 0 , 1 ] , and give conditions that guarantee existence and uniqueness of solution in L p ( [ 0 , 1 ] ), with 1 1 p ∞.We use Banach Fixed Point Theorem and employ the successive approximation method and Chebyshev quadrature for approximating the values of integrals. Finally, to illustrate the results of this work, we provide some numerical examples.
publishDate 2019
dc.date.none.fl_str_mv 2019-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512019000300403
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512019000300403
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2019.020.03.0403
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.20 n.3 2019
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
instacron_str SBMAC
institution SBMAC
reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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