Some applications of Kuratowskis measure of noncopactness

Singh, Kanhaya Lal

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 60 (1976) no. 4, pp. 422-432.

Résumé

In Kuratowski [4] trovasi introdotta la nozione di misura della non compattezza; a questa si legano strettamente i concetti di k-insieme contrazione e di applicazione densificante dovuti rispettivamente a Darbo [2] ed a Furi e Vignoli [3]. Qui nel n. 1 si stabilisce un teorema sulla struttura dei punti fissi di un'applicazione densificante, estendente un risultato di Krasnoselskii e Sobolevskii [14]- Nel n. 2 si ottiene un teorema sulla alternativa di Fredholm per applicazioni densificanti, da cui si derivano quali corollari risultati di Petryshyn [17] e di Nussbaum. Infine, nel n. 3 si stabiliscono teoremi sul punto fisso relativi ad applicazioni densificanti, i quali generalizzano risultati di Vainberg [5] e di Hanani, Netanuahu e Reichaw-Reichbach [16].

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