Abstract
Motivated by the concepts of fuzzy metric and m-metric spaces, we introduced the notion of Non- Archimedean fuzzy m-metric space which is an extension of partial fuzzy metric space. We present some examples in support of this new notion. Regarding this notion, its topological structure and some properties are specified simultaneously. At the end, some fixed point results are also provided.
Highlights
Zadeh [11] was first who introduced the concept of fuzzy sets in 1965
In 1981, the idea of fuzzy contractive mappings was initially introduced by Heilpern [20] and proved some fixed point theorems for these fuzzy contractive mappings in metric linear spaces
A number of fixed point theorems for fuzzy contractive mappings have come into sight
Summary
Zadeh [11] was first who introduced the concept of fuzzy sets in 1965. In 1981, the idea of fuzzy contractive mappings was initially introduced by Heilpern [20] and proved some fixed point theorems for these fuzzy contractive mappings in metric linear spaces. Researchers have great interest in theory of fuzzy metric spaces. Study inquiry into discipline of fixed point theory on fuzzy metric spaces ([2, 5, 8, 15, 20,21,22,23] etc.) has been developed more frequently. The fixed point theory with graph is a very interesting approach in the field of research and has wide number of applications in other fields. In 2008, Jachymski [9] studied the Banach contraction principle in metric space with graph and gave an interesting approach in this direction. Motivated by the work of Jachymski, several authors established many results on various spaces endowed with graph
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