Fixed point theorems in locally convex spaces

T. L. Hicks

Research output: Contribution to journalArticlepeer-review


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 {υn} is given by the Mann iteration process. It is shown that if {υn} 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 lim yn = y.

Original languageEnglish
Pages (from-to)111-115
Number of pages5
JournalPacific Journal of Mathematics
Issue number1
StatePublished - Nov 1978
Externally publishedYes


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