Common Fixed Point Theorem of Semi-Compatible Maps on Intuitionistic Fuzzy Metric Space (original) (raw)
Bharti Mishra, Arun Kumar Garg and Z.K. Ansari, 2023
In present paper, we introduce common property (E.A) in modified intuitionistic fuzzy metric spaces and utilize the same to prove common fixed point theorems in modified intuitionistic fuzzy metric space besides discussing related results and illustrative examples. We are not aware of any paper dealing with same conditions modified intuitionistic fuzzy metric spaces Mathematics Subject Classification (MSC): 47H10, 54H25.
Fixed Point Theorems for Faintly Compatible Mappings in Intuitionistic Fuzzy Metric Space
Journal of the Indian Mathematical Society, 2017
In this paper, we correct the contractive condition of Manro and Kang [16] and prove some common fixed point theorems for four faintly compatible mappings using subsequential continuous mappings in Intuitionistic Fuzzy metric spaces. We also provide an example in support of our main result. Our results improve and generalize the results of Manro and Kang [16].
Semi-Compatible Maps On Intuitionistic Fuzzy Metric Space
IOSR Journal of Mathematics, 2013
In this paper, we prove common fixed point theorem for semi-compatible mappings on intuitionistic fuzzy metric space with different some conditions of Park and Kim ([10], 2008). This research extended and generalized the results of Singh and Chauhan ([14], 2000). The concept of fuzzy set was developed extensively by many authors and used in various fields. Several authors have defined fuzzy metric space Kramosil and Michalek(([5],1975) etc.) with various methods to use this concept in analysis. Jungck (([3],1986), ([4],1988)) researched the more generalized concept compatibility than commutativity and weak commutativity in metric space and proved common fixed point theorems, and Singh and Chauhan ([14],2000) introduced the concept of compatibility in fuzzy metric space and studied common fixed point theorems for four compatible mappings.
Common Fixed Point Theorems in Modified Intuitionistic Fuzzy Metric Spaces
Journal of Applied Mathematics, 2013
This paper consists of main two sections. In the first section, we prove a common fixed point theorem in modified intuitionistic fuzzy metric space by combining the ideas of pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions. In the second section, we prove common fixed point theorems in modified intuitionistic fuzzy metric space from the class of compatible continuous mappings to noncompatible and discontinuous mappings. Lastly, as an application, we prove fixed point theorems using weakly reciprocally continuous noncompatible self-mappings on modified intuitionistic fuzzy metric space satisfying some implicit relations.
Applied Mathematics and Sciences: An International Journal (MathSJ), 2015
In this paper, we give some new definition of Compatible mappings of type (P), type (P-1) and type (P-2) in intuitionistic generalized fuzzy metric spaces and prove Common fixed point theorems for six mappings under the conditions of compatible mappings of type (P-1) and type (P-2) in complete intuitionistic fuzzy metric spaces. Our results intuitionistically fuzzify the result of Muthuraj and Pandiselvi [15]
A Fixed Point Theorem in Modified Intuitionistic Fuzzy Metric Spaces
2013
Fuzzy Mathematics has seen an enormous growth since the introduction of notion of fuzzy sets by Zadeh in 1965. Kramosil and Michalek introduced the notion of fuzzy metric spaces which was later modified by George and Veeramani and others. The notion of intuitionistic fuzzy metric spaces was introduced by Park in 2004. Many authors have studied fixed point and common fixed theorems for mappings on fuzzy metric spaces and intuitionistic fuzzy metric spaces. In this paper we prove a common fixed point theorem for a sequence of mappings in an intuitionistic fuzzy metric space.
2012
The aim of this note is to point out a fallacy in the proof of Theorem 3.1 contained in the recent paper ( Int. J. Contemp. Math. Sci. 5 (2010), 2699-2707) proved in intuitionistic fuzzy metric spaces employing the newly introduced notion of sub-compatible pair of mappings wherein our claim is also substantiated with the aid of an appropriate example. We also rectify the erratic theorem in two ways. In order to avoid repetition and also due to paucity of the space, we assume the terminology and the notations utilized in [6] rather than presenting the same again. For more recent developments, we refer the readers to [1, 3, 9] and references cited therein. The following definitions are essentially contained in [6]. Definition 0.1. Let (X,M,N, ∗, ⋄) be an intuitionistic fuzzy metric space. A pair of self maps (A,S) defined on X is said to be compatible iff lim n→∞ M(ASxn, SAxn, t) = 1 and lim n→∞ N(ASxn, SAxn, t) = 0 wherein {xn} are sequences in X with lim n→∞ Axn = lim n→∞ Sxn = z, z...
Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces
In this paper, utilizing the concept of common limit range property, we prove integral type common fixed point theorems for two pairs of weakly compatible mappings satisfying \phi -contractive conditions in modified intuitionistic fuzzy metric spaces. We give some examples to support the useability of our results. We extend our results to four finite families of self mappings by using the notion of pairwise commuting.
On Fixed-Point Theorems in Intuitionistic Fuzzy Metric Space
International Journal of Open Problems in Computer Science and Mathematics, 2012
In this paper, first we have established two sets of sufficient conditions for a mapping to have unique fixed point in a intuitionistic fuzzy metric space and then we have redefined the contraction mapping in a intuitionistic fuzzy metric space and thereafter we proved the Banach Fixed Point theorem.
Some Fixed Point Theorems in intuitionistic fuzzy metric spaces
Tamkang Journal of Mathematics, 2011
The aim of this paper is to prove some common fixed point theorems by using the property (S-B) and the notion of R-weak commutativity of type (S p) in intuitionistic fuzzy metric spaces. We first formulate the definition of R-weakly commuting mappings of type (S p) in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant's theorem.