The notions of nonexpansive,
contractive, iteratively contractive and strictly contractive mappings have been
generalized to a Hausdorff topological space whose topology is generated by
a family of pseudometrics. A fixed point theorem for strictly contractive
mappings is obtained which generalizes the Banach’s contractive mapping
principle. Several examples and an implicit function theorem are given as well
as some applications in solving functional equations in topological vector
spaces.
For iteratively contractive mappings, some results obtained by D. D. Ang and E.
D. Daykin, S. C. Chu and J. B. Diaz, by M. Edelstein, by K. W. Ng and by E.
Rakotch respectively are generalized.
