Journal of the Australian Mathematical Society

Research Article

Fixed points of quasi-nonexpansive mappings

W. G. Dotson Jra1

a1 North Carolina State University at Raleigh Raleigh, North Carolina.

A self-mapping T of a subset C of a normed linear space is said to be non-expansive provided ║TxTy║ ≦ ║xy║ holds for all x, y xs2208 C. There has been a number of recent results on common fixed points of commutative families of nonexpansive mappings in Banach spaces, for example see DeMarr [6], Browder [3], and Belluce and Kirk [1], [2]. There have also been several recent results concerning common fixed points of two commuting mappings, one of which satisfies some condition like nonexpansiveness while the other is only continuous, for example see DeMarr [5], Jungck [8], Singh [11], [12], and Cano [4]. These results, with the exception of Cano's, have been confined to mappings from the reals to the reals. Some recent results on common fixed points of commuting analytic mappings in the complex plane have also been obtained, for example see Singh [13] and Shields [10].

(Received December 17 1969)