[EN] The purpose of this paper is to provide sufficient conditions for the existence of a unique best proximity point for Geraghty-contractions.Our paper provides an extension of a result due to Geraghty (Proc. Am. Math. Soc. 40:604-608, 1973)

The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to first-order ordinary differential equations.

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Using the classical Schauder fixed point theorem, we prove the existence of solutions of a quadratic integral equation of Fredholm type with supremum in the space of functions satisfying the Hölder condition.

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