Geodesic
On Some Non-Linear Problems
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 394-397

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

Non-linear problems have been studied by Krasnoselski, Browder, and others; in fact Browder and independently Kirk (cf., 1; 5) have proved the following remarkable theorem: let X be a uniformly convex Banach space, U a non-expansive mapping of a bounded closed convex subset C of X into C, i.e., ||Ux — Uy || ⩽ ||x — y|| for x, y ∊ C; then U has a fixed point in C. The aim of this paper is to give some existence theorems for non-linear functional equations in uniformly convex Banach spaces. Similar results may be found in (3 ; 6). 
Srinivasacharyulu, K. On Some Non-Linear Problems. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 394-397. doi: 10.4153/CJM-1968-036-1
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[1] 1. Browder, F. E., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A., 64 (1965), 1041–1044. Google Scholar

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

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