Fixed-point theorems in locally convex spaces

Troy Lee Hicks

Vol. 79 (1978), No. 1, 111–115

DOI: 10.2140/pjm.1978.79.111

Abstract

Let C be a convex subset of a nuclear locally convex space that is also an F-space. Suppose T : C → C is nonexpansive and {v_n} is given by the Mann iteration process. It is shown that if {v_n} is bounded, T has a fixed point. Also, a sequence {y_n} can be constructed such that y_n → y weakly where Ty = y. If C is a linear subspace and T is linear, then limy_n = y.

Mathematical Subject Classification 2000

Primary: 47H10

Milestones

Received: 7 March 1977

Published: 1 November 1978