In this paper, we introduce a new class , which is weaker than a known class , of real continuous functions defined on , and use another method to prove the known unique common fixed point theorem for four mappings with 0, -contractive condition instead of -contractive condition on 2-metric spaces.
In this paper, we consider a countable family of set-valued mappings satisfying some quasi-contractive conditions. We also construct a sequence by the quasi-contractive conditions of mappings and the boundary condition of a closed subset of a metrically convex space, and then prove that the unique limit of the sequence is the unique common fixed point of the mappings. Finally, we give more generalized common fixed point theorems for a countable family of single-valued mappings. The main results generalize and improve many common fixed point theorems for a finite or countable family of single valued or set-valued mappings with quasi-contractive conditions.
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