Remarks on the Belitskii-Lyubich and discrete Markus-Yamabe conjectures

• Autorzy: Sart Frédéric

Identyfikatory

DOI

10.1515/jaa-2022-2013

• Języki publikacji: EN

Abstrakty

EN

In this paperwe prove the Belitskii-Lyubich conjecture for triangular and gradientmappings. These results resemble those obtained for the discrete Markus-Yamabe conjecture. However, the proofs are quite different,which sheds new light on the subject.We complete the picture by showing that the general versions of the two conjectures can be turned into theorems at little cost, simply by relaxing their spectral condition.

Słowa kluczowe

EN

fixed point theorem; global attractor; discrete Markus-Yamabe conjecture; Belitskii-Lyubich conjecture; triangular mapping; gradient mapping

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 1
• Strony: 99--103
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Sart Frédéric

• Terkerkenlaan 21, 9700 Oudenaarde, Belgium

Bibliografia

• [1] G. R. Belitskii and Y. I. Lyubich, Matrix Norms and Their Applications, Oper. Theory Adv. Appl. 36, Birkhäuser, Basel, 1988.
• [2] A. Cima, A. Gasull and F. Mañosas, The discrete Markus-Yamabe problem, Nonlinear Anal. 35 (1999), 343-354.
• [3] A. Cima, A. van den Essen, A. Gasull, E. Hubbers and F. Mañosas, A polynomial counterexample to the Markus-Yamabe conjecture, Adv. Math. 131 (1997), 453-457.
• [4] F. Mañosas and D. Peralta-Salas, Note on the Markus-Yamabe conjecture for gradient dynamical systems, J. Math. Anal. Appl. 322 (2006), 580-586.
• [5] F. Sart, Fair valuation of universal life policies via a replicating portfolio, J. Appl. Anal. 16 (2010), 95-105.
• [6] M. H. Shih and J. W. Wu, Asymptotic stability in the Schauder fixed point theorem, Studia Math. 131 (1998), 143-148.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).