A fixed point theorem for mappings satisfying a general contractive condition of integral type
We analyze the existence of fixed points for mappings defined on complete metric spaces (X,d) satisfying a general contractive inequality of integral type. This condition is analogous to Banach-Caccioppoli's one; in short, we study mappings f:X→X for which there exists a real number c∈]0,1[, su...
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| Language: | English |
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007524 |
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doaj-2dde7864193a4184902d4a2ddd4ab2252020-11-24T20:50:54ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0129953153610.1155/S0161171202007524A fixed point theorem for mappings satisfying a general contractive condition of integral typeA. Branciari0Viale Martiri della Libertà 20, Macerata 62100, ItalyWe analyze the existence of fixed points for mappings defined on complete metric spaces (X,d) satisfying a general contractive inequality of integral type. This condition is analogous to Banach-Caccioppoli's one; in short, we study mappings f:X→X for which there exists a real number c∈]0,1[, such that for each x,y∈X we have ∫0d(fx,fy)φ(t)dt≤c∫0d(x,y)φ(t)dt, where φ:[0,+∞[→[0,+∞] is a Lebesgue-integrable mapping which is summable on each compact subset of [0,+∞[, nonnegative and such that for each ε>0, ∫0εφ(t)dt>0.http://dx.doi.org/10.1155/S0161171202007524 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. Branciari |
| spellingShingle |
A. Branciari A fixed point theorem for mappings satisfying a general contractive condition of integral type International Journal of Mathematics and Mathematical Sciences |
| author_facet |
A. Branciari |
| author_sort |
A. Branciari |
| title |
A fixed point theorem for mappings satisfying a general contractive condition of integral type |
| title_short |
A fixed point theorem for mappings satisfying a general contractive condition of integral type |
| title_full |
A fixed point theorem for mappings satisfying a general contractive condition of integral type |
| title_fullStr |
A fixed point theorem for mappings satisfying a general contractive condition of integral type |
| title_full_unstemmed |
A fixed point theorem for mappings satisfying a general contractive condition of integral type |
| title_sort |
fixed point theorem for mappings satisfying a general contractive condition of integral type |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
We analyze the existence of fixed points for mappings defined on
complete metric spaces (X,d) satisfying a general contractive
inequality of integral type. This condition is analogous to
Banach-Caccioppoli's one; in short, we study mappings f:X→X for which there exists a real number
c∈]0,1[, such that for each x,y∈X we have
∫0d(fx,fy)φ(t)dt≤c∫0d(x,y)φ(t)dt, where φ:[0,+∞[→[0,+∞] is a Lebesgue-integrable mapping which is summable on each compact
subset of [0,+∞[, nonnegative and such that for each
ε>0, ∫0εφ(t)dt>0. |
| url |
http://dx.doi.org/10.1155/S0161171202007524 |
| work_keys_str_mv |
AT abranciari afixedpointtheoremformappingssatisfyingageneralcontractiveconditionofintegraltype AT abranciari fixedpointtheoremformappingssatisfyingageneralcontractiveconditionofintegraltype |
| _version_ |
1716803199311020032 |