Geodesic
A Fixed Point Theorem for Semigroups of Proximately Uniformly Lipschitzian Mappings
Canadian mathematical bulletin, Tome 34 (1991) no. 4, pp. 559-562

Voir la notice de l'article provenant de la source Cambridge University Press

As a generalization of Kiang and Tan's proximately nonexpansive semigroups, the notion of a proximately uniformly Lipschitzian semigroup is introduced and an existence theorem of common fixed points for such a semigroup is proved in a Banach space whose characteristic of convexity is less than one.
DOI : 10.4153/CMB-1991-088-5
Mots-clés : 47H10, Common fixed point, proximately uniformly Lipschitzian semigroup 
Xu, Hong-Kun. A Fixed Point Theorem for Semigroups of Proximately Uniformly Lipschitzian Mappings. Canadian mathematical bulletin, Tome 34 (1991) no. 4, pp. 559-562. doi: 10.4153/CMB-1991-088-5
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[1] 1. Downing, D. and Turett, B., Some properties of the characteristic of convexity relating to fixed point theory, Pacific J. Math. 104 (1984), 343–350. Google Scholar

[2] 2. Edelstein, M. andM. Kiang, T., On ultimately nonexpansive semigroup, Pacific J. Math. 101 (1982), 93–102. Google Scholar

[3] 3. Edelstein, M. andM. Kiang, T., A common fixed point theorem in reflexive locally uniformly convex Banach spaces, Proc. Amer. Math. Soc. 94 (1985), 411–415. Google Scholar

[4] 4. Goebel, K. and Reich, S., Uniform convexity, hyperbolic geometry and nonexpansive mappings. Marcel Dekker, New York-Basel, 1984. Google Scholar

[5] 5. Kiang, M. T., A fixed point theorem for eventually nonexpansive semigroups of mappings, J. Math. Anal. Appl. 56 (1976), 567–569. Google Scholar

[6] 6. Kiang, M. T. and Tan, K. K., Fixed point theorems for proximately nonexpansive semigroups, Canad. Math. Bull. 29 (1986), 160–166. Google Scholar

[7] 7. Lifschitz, E. A., Fixed point theorems for operators in strongly convex spaces, Vornez Gos. Univ. Trudy, Mat. Fak. 10 (1975), 23–28 (in Russian). Google Scholar

[8] 8. Turett, B., A dual view of a theorem of Bâillon, in Nonlinear Analysis and Applications, (S. P. Singh and Burry, L. H., eds.), Marcel Dekker, New York-Basel, 1982, 279–286. Google Scholar

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