Some Common Fixed Point Theorems in Fuzzy b-Metric Space Using Convergent Sequence

Abstract

As the fixed point theory has become one of the interesting field of research in pure mathematics connecting with metric space as well as fuzzy metric spaces. It has explored the new and creative ideas of research activities. One of the most significant extensions of regular metric space is fuzzy metric space. This paper’s goal is to examine the notion of fuzzy b-metric space and using a pair of self mappings to establish some common fixed point results in complete fuzzy b-metric space. These mappings are used in the sequence form of function in fuzzy b-metric space and if this sequence as well as its subsequence converge at a point then this point is the unique common fixed point for these mappings. To demonstrate the strength of our primary finding, a nontrivial example is provided as part of the application. Our findings support a large number of earlier findings in the literature.