Geodesic
Some Fixed Point Theorems in Metric and Banach Spaces
Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 481-491

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

The purpose of this paper is two-fold. Sections 2 and 3 are motivated by an observation that certain theorems concerning "diminishing orbital diameters" (introduced in [1]) are true under weaker assumptions. Specifically, we investigate the relationship between that concept and alternate conditions such as "asymptotic regularity", and in the process we sharpen some metric space results established in [1;5]. Mention is made in these sections of examples which show that certain additional weakenings of our hypotheses cannot be made, but we include in detail only the one which seemed to us most intricate. 
Belluce, L. P.; Kirk, W.A. Some Fixed Point Theorems in Metric and Banach Spaces. Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 481-491. doi: 10.4153/CMB-1969-062-9
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[1] 1. Belluce, L. P. and Kirk, W.A., Fixed point theorems for certain classes of nonexpansive mappings. Proc. Amer. Math. Soc. 20 (1969) 141–146. Google Scholar

[2] 2. Browder, F. E. and Petryshyn, W.V., The solution by iteration of nonlinear functional equations in Banach spaces. Bull. Amer. Math. Soc. 72 (1966) 571–575. Google Scholar

[3] 3. Edelstein, M., On nonexpansive mappings. Proc. Amer. Math. Soc. 15 (1964) 689–695. Google Scholar

[4] 4. Kirk, W.A., A fixed point theorem for mappings which do not increase distances. Amer. Math. Monthly 72 (1965) 1004–1006. Google Scholar

[5] 5. Kirk, W.A., On mappings with diminishing orbital diameters, J. London Math. Soc. 44 (1969) 107–111. Google Scholar

[6] 6. Kirk, W.A., Fixed point theorems for nonexpansive mappings. Proc. Symp. on Nonlinear Functional Analysis, April 1968. (to appear in Symp. Pure Math.) Google Scholar

[7] 7. Kirk, W. A., On a nonlinear functional equation in a Banach space (submitted). Google Scholar

[8] 8. Göhde, D., Zum Prinzip der kontraktiven Abbildung. Math. Nach. 30 (1965) 251–258. Google Scholar

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