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In this paper, we introduce a new class Γ, which is weak than a known class Ψ, of real continuous functions defined on [0, +∞), and use another method to prove the known unique common fixed point theorem for four mappings with γ-contractive condition instead of Ψ-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.