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Zbl 1193.54035
Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces.
(English)
[J] Comput. Math. Appl. 59, No. 9, 3148-3159 (2010). ISSN 0898-1221

Summary: In the first part of this paper, we generalize results on common fixed points in ordered cone metric spaces obtained by {\it I. Altun} and {\it G. Durmaz} [Rend. Circ. Mat. Palermo (2) 58, No. 2, 319--325 (2009; Zbl 1184.54038)] and {\it I. Altun, B. Damnjanović} and {\it D. Djorić} [Appl. Math. Lett. 23, No. 3, 310--316 (2010; Zbl 1197.54052)] by weakening the respective contractive condition. Then, the notions of quasicontraction and $g$-quasicontraction are introduced in the setting of ordered cone metric spaces and respective (common) fixed point theorems are proved. In such a way, known results on quasicontractions and $g$-quasicontractions in metric spaces and cone metric spaces are extended to the setting of ordered cone metric spaces. Examples show that there are cases when new results can be applied, while old ones cannot.
MSC 2000:
*54H25 Fixed-point theorems in topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
65J15 Equations with nonlinear operators (numerical methods)

Keywords: normal and nonnormal cone; ordered cone metric space; quasicontraction; fixed point; common fixed point

Citations: Zbl 1184.54038; Zbl 1197.54052

Cited in: Zbl 1248.54025

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