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Alcune generalizzazioni del Teorema di Browder-Göhde-Kirk

Delfina RouxPaolo Soardi — 1972

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

In this paper we are concerned with applications f , mapping into itself a closed convex subset K of a normed space X , with the property: f ( x ) - f ( y ) a { x - f ( x ) + y - f ( y ) } + b x - y ( a , b not necessarily constants, a 0 , b 0 , 2 a + b 1 ). We prove that a fixed point of f exists in K under the following assumptions: 1) is uniformly convex and in there exists a point with bounded orbit; 2) X is a Banach space, K is weakly compact, f is continuous and sup x , y K b ( x , y ) < 1 . Thereafter, if X is strictly convex, we prove that the set of all fixed points of f in K is closed...

Symbolic calculus in A(G). Nota II

Leonede De MichelePaolo Soardi — 1974

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Si dimostra che solo le funzioni reali analitiche operano nell'algebra A(G) se G è un gruppo abeliano infinito, oppure un gruppo mediabile discreto con sottogruppi abeliani arbitrariamente grandi, oppure un gruppo di Lie non discreto.

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