Continuation results for mappings of contractive type

We survey fixed point results for mappings of contractive type in metric spaces, quasiuniform and uniform spaces and, more general, in syntopogenous spaces. The results involve usual contractions, non-expansive mappings, Caristi type mappings and generalized contractions. The focus is on the continuation theory for such types of mappings. We stress on our own results which have been obtained since 1980. For the reader convenience, some of the results which appeared in less accessible publications are here presented together with their proofs.

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

contraction; nonexpansive mapping; generalized contraction; fixed point; continuation; metric space; uniform space; syntopogenous space.

R. Precup, Continuation results for mappings of contractive type, Seminar on Fixed Point Theory Cluj-Napoca 2 (2001), 23-40.

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