RGNAA PublishingCommunications in Nonlinear Analysis2371-79208120200601COINCIDENCE POINTS WITH φ-CONTRACTIONS IN PARTIALLY ORDERED FUZZY METRIC SPACES114111011ENPradyutDasIndian Institute Of Engineering Science and Technology, ShibpurBinayak SChoudhuryIndian Institute of Engineering Science and Technology, ShibpurParbatiSahaIndian Institute of Engineering Science and Technology, ShibpurSamir KumarBhandariBajkul Milani MahavidyalayaJournal Article20200421In this paper our main result is a coupled coincidence point theorem for a compatible pair<br />in a fuzzy metric space with a partial ordering under the assumption of a new coupled contraction inequality which involves a recently introduced control function which is a generalization of<br />many such functions previously used in literatures. The proof depends on a lemma in which we<br />prove a condition for simultaneous holding of Cauchy criteria for two sequences. We use H-type<br />t-norms in this paper in order to utilize the equi-continuity of the t-norm iterates in the proof<br />of the lemma. The contraction inequality also involves another function which is borrowed from<br />a recent work, there is a partial ordering defined on the fuzzy metric space. There are several<br />corollaries of the main theorem. An illustrative example is given.