COINCIDENCE POINTS WITH φ-CONTRACTIONS IN PARTIALLY ORDERED FUZZY METRIC SPACES

Document Type: Original Article

Authors

1 Indian Institute Of Engineering Science and Technology, Shibpur

2 Indian Institute of Engineering Science and Technology, Shibpur

3 Bajkul Milani Mahavidyalaya

Abstract

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.

Keywords


Articles in Press, Accepted Manuscript
Available Online from 26 July 2020