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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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |