Abstract
AbstractWe prove some coupled fixed point theorems for mappings satisfying different contractive conditions on complete cone metric spaces.
Highlights
Huang and Zhang in 1 generalized the concept of metric spaces by considering vector-valued metrics cone metrics with values in an ordered real Banach space. They proved some fixed point theorems in cone metric spaces showing that metric spaces really doesnot provide enough space for the fixed point theory. They gave an example of a cone metric space X, d and proved existence of a unique fixed point for a selfmap T of X which is contractive in the category of cone metric spaces but is not contractive in the category of metric spaces
Regarding the concept of coupled fixed point, introduced by Bhaskar and Lakshmikantham 10, we consider the corresponding definition for the mappings on complete cone metric spaces and prove some coupled fixed point theorems
See [4, 6, 7, 9] for more related results about complete cone metric spaces and fixed point theorems for different types of mappings on these spaces
Summary
We prove some coupled fixed point theorems for mappings satisfying different contractive conditions on complete cone metric spaces.
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