0*, Shailesh Dhar Diwan**

Periodicity:April - June'2016

DOI : https://doi.org/10.26634/jmat.5.2.6007

* Senior Assistant Professor, Department of Applied Mathematics, SSIPMT, Raipur, India.

** Associate Professor, Department of Mathematics, Government P. G. College, Dhamtari, India.

DOI : https://doi.org/10.26634/jmat.5.2.6007

In this paper, the authors have established some common fixed point theorems in fuzzy metric spaces using the Common Limit in the Range (i.e, (CLRg )) property. Since, CLRg property does not require condition of closeness of range and so the results extend, generalize and improve several known results of metric spaces and fuzzy metric space in several ways. The obtained results show that the completeness of space and continuity of mappings are not required. In the case of CLRg property, Containment of ranges of involved mappings and the closeness of subspace are not required. As an application to the main result, the authors present some fixed point theorems for self mappings in fuzzy metric space by using the notion of (EA) property. The (EA) property replaces the completeness requirement of the space with a more natural condition of closeness of the range. The (EA) property also relaxes the continuity of one or more mappings and containment of the range of one mapping into the range of another, which can be used to construct the sequences of some iterates. Some examples are furnished in the paper to support the validity of the results.

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