On the continuation method and the nonlinear alternative for Caristi-type non-self-mappings


In this note we survey some continuation fixed point theorems for Caristi-type non-self-mappings on complete metric spaces. Two new results, a continuation theorem and the nonlinear alternative are given in terms of retractions and generalized Leray–Schauder conditions.


Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Caristi’s theorem; continuation results; nonlinear alternative; contraction; metric space; retraction; fixed point.

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R. Precup, On the continuation method and the nonlinear alternative for Caristi-type non-self-mappings, J. Fixed Point Theory Appl. 16 (2014), 3-10, https://doi.org/10.1007/S11784-014-0197-9


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Journal of Fixed Point Theory and Applications

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