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Rotative mappings in metric spaces of hyperbolic type

Górnicki J., Pupka K.

Journal of Mathematics and Applications

2006

Vol. 28

49-70

The aim of this paper is to give some conditions providing existence of fixed points for k-lipschitzian and uniformly k-lipschitzian mappings which are n-rotative with n ≥ 2 in complete metric spaces of hyperbolic type.

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

Pupka K.

Demonstratio Mathematica

2006

Vol. 39, nr 2

455-463

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.

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

Górnicki J., Pupka K.

Demonstratio Mathematica

2005

Vol. 38, nr 2

431--435

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.