Vol. 99, No. 2, 1982

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A fixed point theorem for product spaces

Ali Ahmad Fora

Vol. 99 (1982), No. 2, 327–335
Abstract

We prove the following result in this paper: Let (X,d) be a complete metric space and Y be a space having the fixed point property. Let f : X × Y X × Y be a continuous map. If f is a contraction mapping in the first variable, then f has a fixed point.

This result is a generalization to the result obtained in Nadler [5].

Other results are proved concerning the fixed point theorem for product spaces.

The concept “continuous height-selection” is discussed and its relation to the existence of fixed points for a function is also discussed.

Mathematical Subject Classification 2000
Primary: 54H25
Milestones
Received: 10 December 1979
Revised: 6 April 1981
Published: 1 April 1982
Authors
Ali Ahmad Fora