Common coupled fixed point theorems in cone metric spaces for w-compatible mappings
نویسندگان
چکیده
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 having non-empty interior. Coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend and unify several well known comparable results in the literature. Results are supported by three examples. Cone metric spaces were introduced by Huang and Zhang in [11], where they investigated the convergence in cone metric spaces, introduced the notion of their completeness, and proved some fixed point theorems for contractive mappings on these spaces. Recently, in [1–19] some common fixed point theorems have been proved for maps on cone metric spaces. However, in [1,2,11–13], the authors usually obtain their results for normal cones. For more results in cone metric space we, refer to ([4–7,18,20] and references mentioned therein). In this paper we do not impose the normality condition for the cones. The only assumption is that the interior of the cone P is non-empty, so we use neither continuity of the vector metric d, nor Sandwich Theorem. Following definitions and results will be needed in the sequel.
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ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 217 شماره
صفحات -
تاریخ انتشار 2010