Remarks on fixed points of involutions of order n>2 in Hilbert spaces

• Autorzy: Pupka K.
• Języki publikacji: EN

Abstrakty

EN

Suppose that C is a nonempty bounded closed and a convex subset of a Hilbert space H and T: C -> C is k-lipschitzian or uniformly k-lipschitzian mapping which has the property that, for some n > 1, Tn is the identity. The author determines a function ko(n) > 1 such that for k < ko(n) mapping T has a fixed points in C.

Słowa kluczowe

EN

involutions; fixed points; Lipchitzian mappings; Hilbert space

PL

punkty stałe; potęgowania; odwzorowania Lipchitziana; przestrzeń Hilberta

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 2
• Strony: 455--463
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Pupka K.

• Department of Mathematics, Rzeszów University of Technology, P. O. Box 85, 35-959 Rzeszów, Poland,

Bibliografia

• [1] K. Goebel, Convexity of balls and fixed-point theorems for mappings with nonexpansive square, Compositio Math. 22 (1970), 269-274.
• [2] K. Goebel, E. Złotkiewicz, Some fixed point theorems in Banach spaces, Coll. Math. 23 (1971), 103-106.
• [3] J. Górnicki, Fixed points of involution, Math. Japonica, 43, no. 1 (1996), 151-155.
• [4] J. Górnicki, K. Pupka, Remarks on fixed points for involutions of order n = 3 in Banach spaces, Demonstratio Math. 38 (2) (2005), 431-435.
• [5] J. Górnicki, K. Pupka, Fixed point theorems for n-periodic mappings in Banach spaces, Comment. Math. Univ. Carolinae 46, 1 (2005), 33-42.
• [6] W. A. Kirk, A fixed point theorem for mappings with a nonexpansive iterate, Proc. Amer. Math. Soc. 29 (1971), 294-298.
• [7] W. A. Kirk, B. Sims (eds.), Handbook of Metric Fixed Point Theory, Kluwer Acad. Publ., Dordrecht-Boston-London, 2001.
• [8] M. Koter-Mórgowska, Rotative mappings in Hilbert space, J. Nonlinear and Convex Analysis 1, no 3 (2000), 295-304.
• [9] J. Linhar, Fixpunkte von Involutionen n-ter Ordnung, ¨ Osterreich. Akad. Wiss. Math.-Natur. kl. II, 180 (1973), 89-93.