We introduce the notion of λ-spaces which is much weaker than cone metric spaces defined by Huang and X. Zhang 2007. We establish some critical point theorems in the setting of λ-spaces and, in particular, in the setting of complete cone metric spaces. Our results generalize the critical point theorem proposed by Dancs et al. 1983 and the results given by Khanh and Quy 2010 to λ-spaces and cone metric spaces. As applications of our results, we characterize the completeness of λ-space cone metric spaces and quasimetric spaces are special cases of λ-space and studying the Ekeland type variational principle for single variable vector-valued functions as well as for multivalued bifunctions in the setting of cone metric spaces.

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