A contribution to fixed point theory in quasi-metric spaces. (English) Zbl 0814.47061

Jachymski, Jacek

Publ. Math. Debr. 43, No. 3-4, 283-288 (1993).

This article is devoted to the proof of the fixed point theorem for an operator \(T\) satisfying the following condition \[ d(T^ p x, Ty)\leq h\max \{d(y, T^ i x),d(T^ i x, Ty), d(T^ i x, T^ j y), d(y, Ty): 0\leq i,\;j\leq p\} (x, y\in \mathbb{X}) \] with \(h< 1\) in the complete quasi- metric (‘metric’ without symmetry property) space \(\mathbb{X}\).

Reviewer: P.Zabreiko (Minsk)

MSC:

47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10	Fixed-point theorems
54H25	Fixed-point and coincidence theorems (topological aspects)

Keywords:

fixed point theorem; complete quasi-metric