Abstract
We mainly focus on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in fuzzy metric spaces. Our results provide a novel research direction for fixed point theory in fuzzy metric spaces as well as a substantial extension of several important results from classical metric spaces.
Highlights
Fixed point theory of classical metric spaces plays an important role in general topology
According to fuzzy Banach contraction theorem of complete fuzzy metric space in the sense of Grabiec [1], we can obtain the following lemma
If the following conditions are satisfied: (i) Tnm is a contraction mapping for a certain m = m(n), (ii) {Tn} converges pointwise to T0 and {Tn} is a uniformly equicontinuous sequence, (iii) Tnxn = xn, n = 0, 1, 2, 3, . . ., the sequence {xn} converges to x0; that is, xn → x0
Summary
Fixed point theory of classical metric spaces plays an important role in general topology. According to fuzzy Banach contraction theorem of complete fuzzy metric space in the sense of Grabiec [1], we can obtain the following lemma.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
