Common fixed points of a generalized ordered g-quasicontraction in partially ordered metric spaces

Abstract

The concept of a generalized ordered g-quasicontraction is introduced, and some fixed and common fixed point theorems for a g-nondecreasing generalized ordered g-quasicontraction mapping in partially ordered complete metric spaces are proved. We also show the uniqueness of the common fixed point in the case of a generalized ordered g-quasicontraction mapping. Finally, we prove fixed point theorems for mappings satisfying the so-called weak contractive conditions in the setting of a partially ordered metric space. Presented theorems are generalizations of very recent fixed point theorems due to Golubović et al. (Fixed Point Theory Appl. 2012:20, 2012). MSC: 47H10, 47N10. © 2013 Liu and Ješić; licensee Springer.