A fixed point theorem for mappings satisfying a general contractive condition of integral type

A. Branciari

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 29, 1-6

Abstract:

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 ∫ 0 d ( f x , f y ) φ ( t ) d t ≤ c ∫ 0 d ( x , y ) φ ( t ) d t , 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 , ∫ 0 ε φ ( t ) d t > 0 .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:641824

DOI: 10.1155/S0161171202007524

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