Uniformly normal structure and uniformly Lipschitzian semigroups |
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| Authors: | Lu-Chuan Ceng Jen-Chih Yao |
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| Institution: | a Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, Chinab Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwanc Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia |
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| Abstract: | Assume that X is a real Banach space with uniformly normal structure and C is a nonempty closed convex subset of X. We show that a κ-uniformly Lipschitzian semigroup of nonlinear self-mappings of C admits a common fixed point if the semigroup has a bounded orbit and if κ is appropriately greater than one. This result applies, in particular, to the framework of uniformly convex Banach spaces. |
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| Keywords: | 47H09 47H10 47H20 |
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