© Hindawi Publishing Corp. 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 analo-gous 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 ∫d(fx,fy)0 ϕ(t)dt ≤ c ∫d(x,y) 0 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, ∫ ε 0 ϕ(t)dt> 0. 2000 Mathematics Subject Classification: 54H25, 47H10. 1. Introduction. Th