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Abstract: 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. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of α – ψ ϕ -contractive and cyclic α – ψ ϕ -contractive mappings and establish the existence and uniqueness of fixed points for such mappings in complete metric-like spaces. The results presented here substantially generalize and extend several comparable results in the existing literature, in particular those of Karapinar and Salimi (2013). As an application, we prove new fixed point results for ψ ϕ -graphic and cyclic ψ ϕ -graphic contractive mappings. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]