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


Journal of Applied & Computational Mathematics

Author(s): A Branciari

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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

This article was published in International Journal of Mathematics and Mathematical Sciences and referenced in Journal of Applied & Computational Mathematics

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