Vol. 79, No. 1, 1978

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Fixed-point theorems in locally convex spaces

Troy Lee Hicks

Vol. 79 (1978), No. 1, 111–115
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 {vn} is given by the Mann iteration process. It is shown that if {vn} is bounded, T has a fixed point. Also, a sequence {yn} can be constructed such that yn y weakly where Ty = y. If C is a linear subspace and T is linear, then limyn = y.

Mathematical Subject Classification 2000
Primary: 47H10
Milestones
Received: 7 March 1977
Published: 1 November 1978
Authors
Troy Lee Hicks