A generalization of Hegedüs-Szilágyi’s fixed point theorem in complete metric spaces
نویسنده
چکیده
Theorem 1 (Theorem 5 in [1]) Let (X,d) be a complete metric space, and let T be a mapping on X. Assume DT (x) <∞ for all x ∈ X. Assume also that there exists a function φ from [0,∞) into itself satisfying the following: (i) φ(t) < t holds for all t ∈ (0,∞); (ii) φ is upper semicontinuous from the right; (iii) d(Tx,Ty)≤ φ ◦DT (x, y) holds for all x, y ∈ X . Then T has a unique fixed point z.Moreover, {Tnx} converges to z for any x ∈ X.
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تاریخ انتشار 2018