MR3104897 Reviewed Mawhin, J. Variations on some finite-dimensional fixed-point theorems. Translation of Ukraïn. Mat. Zh. 65 (2013), no. 2, 266–272. Ukrainian Math. J. 65 (2013), no. 2, 294–301. (Reviewer: Calogero Vetro) 54H25 (47H10)

Abstract

Inglese:The author presents an interesting discussion on three fundamental results in the literature and related theory: the Poincaré-Miranda theorem [C. Miranda, Boll. Un. Mat. Ital. (2) 3 (1940), 5–7; MR0004775 (3,60b)], the Pireddu-Zanolin fixed point theorem [M. Pireddu and F. Zanolin, Topol. Methods Nonlinear Anal. 30 (2007), no. 2, 279–319; MR2387829 (2009a:37032)] and the Zgliczyński fixed point theorem [P. Zgliczyński, Nonlinear Anal. 46 (2001), no. 7, Ser. A: Theory Methods, 1039–1062; MR1866738 (2002h:37032)]. The author provides generalizations of the last two fixed point theorems by using the original technique that he developed in a previous paper and the Poincaré-Miranda theorem, respectively. The proofs presented have the merit of being short and elegant.