Remarks on fixed points for involutions of order n=3 in Banach space

• Autorzy: Górnicki J. , Pupka K.
• Języki publikacji: EN

Abstrakty

EN

In this paper we study the problem of existence of fixed points of k-Lipschitzian and uniformly k-Lipschitzian mappings (k > 1) denned on nonempty closed convex subset of Banach space. Using very simple method we extend Kirk and Linhart's result [5, 8] in the case of involution of order n = 3.

Słowa kluczowe

EN

Lipchitzian mappings; involutions; fixed points

PL

odwzorowanie Lipchitziana; przestrzeń Banacha; punkt stały; potęgowania

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 431--435
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Górnicki J.

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

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] J. Górnicki, Fixed points for Lipschitzian involutios of order n=3, Zeszyty Nauk. Polit. Rzeszowskiej, seria: Matematyka i Fizyka, z. 12 (1991), 115-119.
• [3] J. Górnicki, Fixed points of involution, Math. Japonica, 43, no. 1 (1996), 151-155.
• [4] B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967), 957- 961.
• [5] W. A. Kirk, A fixed point theorem for mappings with a nonexpansive iterate, Proc. Amer. Math. Soc. 29 (1971), 294-298.
• [6] W. A. Kirk, B. Sims (eds.), Handbook of Metric Fixed Point Theory, Kluwer Acad. Publ., Dordrecht-Boston-London, 2001.
• [7] M. Koter-Mórgowska, Rotative mappings in Hilbert space, J. Nonlinear and Convex Anal. 1, no 3 (2000), 295-304.
• [8] J. Linhart, Fixpunkte von Involutionen n - ter Ordnung, Österreich. Akad. Wiss. Math. - Natur. kl. II, 180 (1973), 89-93.