Premium
Some results on implicit contractive conditions in metric spaces endowed with arbitrary binary relations
Author(s) -
Chuensupantharat Nantaporn,
Kumam Poom
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4861
Subject(s) - mathematics , corollary , coincidence , metric space , coincidence point , binary relation , pure mathematics , banach space , contraction principle , contraction (grammar) , binary number , fixed point theorem , discrete mathematics , arithmetic , medicine , alternative medicine , pathology
The main purpose of this study is to establish some coincidence and common fixed point theorems for 2 self‐mappings via the condition of implicit function on metric spaces provided with arbitrary binary relation. In our results, the main theorems are the generalized version of the literatures, and we also give some examples to guarantee our main results. Moreover, we show that the result to guarantee a coincidence point which are more useful than the previous results of Banach's contraction which cannot be applied. Furthermore, we include some consequences for proving the corollary, which satisfied several well‐known contractions that are obtained from the main results.