University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065410420130830Fixed point theory for cyclic $\varphi$-contractions in fuzzy metric spaces125133105210.22111/ijfs.2013.1052ENYong-hongShenSchool of Mathematics and Statistics, Tianshui Normal Univer-
sity, Tianshui 741001, People's Republic of ChinaDongQiuCollege of Mathematics and Physics, Chongqing University of Posts and
Telecommunications, Chongqing 400065, People's Republic of ChinaWeiChenSchool of Information, Capital University of Economics and Business,
Beijing, 100070, People's Republic of ChinaJournal Article20111207In this paper, the notion of cyclic $\varphi$-contraction in fuzzy<br />metric spaces is introduced and a fixed point theorem for this type<br />of mapping is established. Meantime, an example is provided to<br />illustrate this theorem. The main result shows that a self-mapping<br />on a G-complete fuzzy metric space has a unique fixed point if it<br />satisfies the cyclic $\varphi$-contraction. Afterwards, some results in<br />connection with the fixed point are given.https://ijfs.usb.ac.ir/article_1052_bef858d33cac8adb4eaaa9d48f565200.pdf