Abstract
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.
Highlights
At first, we give well known definitions and results
If w = fx = gx for some x X, x is called a coincidence point of f and g, and w is called a point of coincidence of f and g
The following is the main conclusion in this paper
Summary
We give well known definitions and results. Open AccessDefinition ric space XDefinition 1.3. be convergent to ([5,6]) x X ,A if sequence for each a xnX n , is said to limn d xn , x, a 0 .And write xn x and call x the limit of xn n .Definition 1.4. ([5,6]) A 2-metric space X , d is said to be complete, if every cauchy sequence in X is convergent.Definition 1.5. ([7,8]) Let f and g be two selfmappings on a set X. The second author has obtained an unique common fixed point theorem for four mappings with -contrac- tive condition [1,2] on 2-metric spaces in [1], where is a continuous and non-decreasing real function on 0, satisfying that t < t for all t > 0 . We introduce a new class of real functions defined on 0, , and reprove the well known unique common fixed point theorem for four mappings with -contractive condition replaced by -contractive condition on 2-metric spaces.
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