Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces

Cho, Yeol Je; Sedghi, Shaban; Shobe, Nabi

doi:10.1016/j.chaos.2007.06.108

Cited by 19 publications

(13 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As an application to our main result, we present a common fixed point theorem for two finite families of self mappings in fuzzy metric space using the notion of pairwise commuting due to Imdad et al [15]. Our results improve and generalize the results of Cho et al [26], Abbas et al [7] and Kumar [8]. …”

Section: Introductionsupporting

confidence: 66%

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

Chauhan¹,

Sintunavarat²,

Kumam³

2012

View full text Add to dashboard Cite

In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, "Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces," Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244 and several known results existing in the literature.

show abstract

Section: Introductionsupporting

confidence: 66%

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

Chauhan¹,

Sintunavarat²,

Kumam³

2012

View full text Add to dashboard Cite

show abstract

“…Although the space F cc (R) is not a vector space, the Hahn-Banach extension theorems on F cc (R) still can be studied by referring to Wu [7]. On the other hand, the fixed point theorems in fuzzy metric space have been studied in [8][9][10][11][12][13][14][15][16][17][18][19]. However, the fuzzy metric space is completely different from the near metric space of fuzzy numbers that is adopted in this paper.…”

Section: Introductionmentioning

confidence: 99%

Near Fixed Point Theorems in the Space of Fuzzy Numbers

2018

Mathematics

View full text Add to dashboard Cite

Abstract:The fuzzy numbers are fuzzy sets owning some elegant mathematical structures. The space consisting of all fuzzy numbers cannot form a vector space because it lacks the concept of the additive inverse element. In other words, the space of fuzzy numbers cannot be a normed space even though the normed structure can be defined on this space. This also says that the fixed point theorems established in the normed space cannot apply directly to the space of fuzzy numbers. The purpose of this paper is to propose the concept of near fixed point in the space of fuzzy numbers and to study its existence. In order to consider the contraction of fuzzy-number-valued function, the concepts of near metric space and near normed space of fuzzy numbers are proposed based on the almost identical concept. The concepts of Cauchy sequences in near metric space and near normed space of fuzzy numbers are also proposed. Under these settings, the existence of near fixed points of fuzzy-number-valued contraction function in complete near metric space and near Banach space of fuzzy numbers are established.

show abstract

“…In [ [6], [7]], George and Veeramani introduced and studied the notion of fuzzy metric spaces that constitutes a modification of the one due to Kramosil and Michalek. Many authors have contributed to the development of this theory and apply to fixed point theory, for instance [1,[3][4][5]8,10,11,15,16,[18][19][20]22,[24][25][26][27]. In 1976, Jungck [12] introduced the notion of commuting mappings.…”

Section: Introductionmentioning

confidence: 99%

Weakly Compatible Mappings along with $CLR_{S}$ property in Fuzzy Metric Spaces

Manro¹,

Bhatia²,

Kumar³

et al. 2013

Journal of Nonlinear Analysis and Application

View full text Add to dashboard Cite

The aim of this work is to use newly introduced property, which is so called "common limit in the range (CLR S )" for four self-mappings, and prove some theorems which satisfy this property. Moreover, we establish some new existence of a common fixed point theorem for generalized contractive mappings in fuzzy metric spaces by using this new property and give some examples to support our results. Ours results does not require condition of closeness of range and so our theorems generalize, unify, and extend many results in literature. Our results improve and extend the results of Cho et al.

show abstract

Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces

Cited by 19 publications

References 28 publications

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

Near Fixed Point Theorems in the Space of Fuzzy Numbers

Weakly Compatible Mappings along with $CLR_{S}$ property in Fuzzy Metric Spaces

Contact Info

Product

Resources

About