Some common fixed point theorems for sequence of self mappings in fuzzy metric space with property (CLRg)

Abstract

In this research article we generalize and improve the results of K. Jha and V. Pant [K. Jha and V. Pant, Some Common fixed point theorem in fuzzy metric space with property (E.A.), Thai Journal of Mathematics, Vol 15, No.1 (2017), 217-226] using weak compatible maps along with property (CLRg).We also demonstrate an example in support of our main result. K.Jha and V.Pant proved their main result that is Theorem-A by applying the concept of property (E-A),to prove this result they take closeness of range of subspaces that is they proved their main result by using stronger contractive conditions, while in this paper we prove the same result as a Theorem 3.1 by removing the condition of ‘closeness of range of subspaces’ and instead of applying the concept of property (E-A) we do apply the concept of property (CLRg).The importance of property ‘CLR’(Common Limit in Range) ensures that one does not require the closeness of range subspaces. That is we prove the same result for a weaker contractive conditions. By proving the result as Theorem-A, Jha and Pant improved and generalized many similar results on fixed points. The purpose of this paper is to further improve and generalize the result of Jha and Pant and some earlier similar results on fixed point.