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Keywords: Coupled common fixed point Coupled coincidence point Coupled point of coincidence Cone metric space Normal and non-normal cone a b s t r a c t In this paper we introduce the concept of a w-compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in cone metric space with a cone… (More)
Recommended by Mohamed Khamsi We prove several fixed point theorems on cone metric spaces in which the cone does not need to be normal.
New fixed point results for a pair of non-self mappings defined on a closed subset of a metrically convex cone metric space which is not necessarily normal are obtained. By adapting Assad-Kirk's method the existence of a unique common fixed point for a pair of non-self mappings is proved, using only the assumption that the cone interior is nonempty.… (More)
Cone metric spaces and fixed point theorems of T-Kannan contractive mappings, Int. J. Math. Anal. 4 (4) (2010) 175–184] proved fixed point theorems for T-Kannan and T-Chatterjea contractions in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this without using the normality condition. Two results for these classes of… (More)