Coincidence Points with φ-Contractions in Partially Ordered Fuzzy Metric Spaces

Document Type : Original Article


1 Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Shibpur, Howrah - 711103, West Bengal, India

2 Department of Mathematics, Bajkul Milani Mahavidyalaya, P.O-Kismat Bajkul, Purba Medinipur, Pin- 721655, West-Bengal, India


In this paper our main result is a coupled coincidence point theorem for a compatible pair
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
many such functions previously used in literatures. The proof depends on a lemma in which we
prove a condition for simultaneous holding of Cauchy criteria for two sequences. We use H-type
t-norms in this paper in order to utilize the equi-continuity of the t-norm iterates in the proof
of the lemma. The contraction inequality also involves another function which is borrowed from
a recent work, there is a partial ordering defined on the fuzzy metric space. There are several
corollaries of the main theorem. An illustrative example is given.