Fixed Point Theorem In Fuzzy 3-Metric Space

Mathematical Theory and Modeling, 2013

In this paper, we give some new definitions of compatible mappings of types (I) and (II) in fuzzy-2 metric space and fuzzy-3 metric space prove some common fixed point theorems for mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy-2 metric space and fuzzy-3 metric space. Our results extend, generalize and improve the corresponding results given by many authors.

Kyungpook mathematical journal, 2011

Related fixed point theorems on two or three metric spaces have been proved in different ways.However, so for the related fixed point theorem on fuzzy metric spaces have not been proved. Sharma, Deshpande and Thakur were the first who have established related fixed point theorem for four mappings on two complete fuzzy metric spaces. Their work was maiden in this line. In this paper we obtain a related fixed point theorem for six mappings on three complete fuzzy metric spaces. Of course this is a new result on this line.

International Journal of Fuzzy Mathematical Archive

The purpose of this paper is to prove some common fixed point theorems in fuzzy-2, fuzzy-3 metric spaces by employing the notion of semi-compatible and reciprocal continuity. We extend and generalize the result of Chauhan et al. [1] and Som [19] from fuzzy metric spaces to fuzzy-2 metric and fuzzy-3 metric Spaces.

Fixed Point Theory and Applications, 2013

In this paper we prove an existence and uniqueness theorem for contractive type mappings in fuzzy metric spaces. In order to do that, we consider a slight modification of the concept of a tripled fixed point introduced by Berinde et al. (Nonlinear Anal. TMA 74:4889-4897, 2011) for nonlinear mappings. Additionally, we obtain some fixed point theorems for metric spaces. These results generalize, extend and unify several classical and very recent related results in literature. For instance, we obtain an extension of Theorem 4.1 in (Zhu and Xiao in Nonlinear Anal. TMA 74:5475-5479, 2011) and a version in non-partially ordered sets of Theorem 2.2 in (Bhaskar and Lakshmikantham in Nonlinear Anal. TMA 65:1379-1393. As application, we solve a kind of Lipschitzian systems in three variables and an integral system. Finally, examples to support our results are also given.

2016

In this paper, we are proving a common fixed point theorem for mappings satisfying common E.A. like property in fuzzy 2-metric spaces, which improves and generalize result of Yadav and Thakur [5].