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.