Fixed point theorems for mappings with a contractive iterate at a point
Author: L. F. Guseman
Journal: Proc. Amer. Math. Soc. 26 (1970), 615-618
MSC: Primary 47.85; Secondary 54.00
MathSciNet review: 0266010
Abstract: In a recent paper, V. M. Sehgal discussed continuous self-mappings of a complete metric space with a contractive iterate at each point of the space. Sehgal showed that such mappings have a unique fixed point and the sequence of iterates of any point in the space converges to the fixed point. In the present paper, the result of Sehgal is generalized to mappings which are not necessarily continuous and which have a contractive iterate at each point in a (possibly proper) subset of the space.
Keywords: Fixed points, contraction mapping, contractive iterate, contractive iterate at a point, sequence of iterates
Article copyright: © Copyright 1970 American Mathematical Society