Fixed point theorems for nonexpansive mappings

Abstract

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. © 1972 Pacific Journal of Mathematics.