Fixed Point Theorems In Locally Convex Spaces
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 {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. © 1978 by Pacific Journal of Mathematics.
Recommended Citation
T. L. Hicks, "Fixed Point Theorems In Locally Convex Spaces," Pacific Journal of Mathematics, vol. 79, no. 1, pp. 111 - 115, Mathematical Sciences Publishers (MSP), Jan 1978.
The definitive version is available at https://doi.org/10.2140/pjm.1978.79.111
Department(s)
Mathematics and Statistics
International Standard Serial Number (ISSN)
0030-8730
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 Mathematical Sciences Publishers (MSP), All rights reserved.
Publication Date
01 Jan 1978
