Common fixed point theorems in -fuzzy metric spaces
Section snippets
Introduction and preliminaries
The notion of fuzzy sets was introduced by Zadeh [18]. Various concepts of fuzzy metric spaces were considered in [6], [7], [12], [13]. Many authors have studied fixed theory in fuzzy metric spaces. The most interesting references are [2], [3], [10], [11], [15], [16].
In the sequel, we shall adopt usual terminology, notation and conventions of -fuzzy metric spaces introduced by Saadati et al. [17]. Definition 1.1 Let be a complete lattice, and U a non-empty set called universe. An -fuzzy set on U[10]
The main results
Theorem 2.1 Let {An} be a sequence of mappings Ai of a complete -fuzzy metric space which has the property (C), into itself such that, for any two mappings Ai, Aj,for some m; here 0 < αi,j < k < 1 for i, j = 1, 2, … , x, y ∈ X and t > 0. Then the sequence {An} has a unique common fixed point in X. Proof Let x0 be an arbitrary point in X and define a sequence {xn} in X by . Then we have
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