Common Fixed Point Theorems for a Pair of Self-Mappings in Fuzzy Cone Metric Spaces

Rehman, Saif Ur; Li, Yongjin; Jabeen, Shamoona; Mahmood, Tayyab

doi:10.1155/2019/2841606

Cited by 6 publications

(4 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They presented some basic properties and a fuzzy cone Banach contraction theorem in a fuzzy cone metric space with the assumption that fuzzy cone contractive sequences are Cauchy. Some more properties and fixed point results in FCM-spaces can be found (e.g., see [21][22][23][24][25][26] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Weakly compatible and quasi-contraction results in fuzzy cone metric spaces with application to the Urysohn type integral equations

2020

View full text Add to dashboard Cite

In this paper, we present some weakly compatible and quasi-contraction results for self-mappings in fuzzy cone metric spaces and prove some coincidence point and common fixed point theorems in the said space. Moreover, we use two Urysohn type integral equations to get the existence theorem for common solution to support our results. The two Urysohn type integral equations are as follows: $$\begin{aligned} &x(l)= \int _{0}^{1}K_{1}\bigl(l,v,x(v) \bigr)\,dv+g(l), \\ &y(l)= \int _{0}^{1}K_{2}\bigl(l,v,y(v) \bigr)\,dv+g(l), \end{aligned}$$ x(l)=∫01K1(l,v,x(v))dv+g(l),y(l)=∫01K2(l,v,y(v))dv+g(l), where $l\in [0,1]$l∈[0,1] and $x,y,g\in \mathbf{E}$x,y,g∈E, where E is a real Banach space and $K_{1},K_{2}:[0,1]\times [0,1]\times \mathbb{R}\to \mathbb{R}$K1,K2:[0,1]×[0,1]×R→R.

show abstract

Section: Introductionmentioning

confidence: 99%

Weakly compatible and quasi-contraction results in fuzzy cone metric spaces with application to the Urysohn type integral equations

2020

View full text Add to dashboard Cite

show abstract

“…They analysed convergence and substituted real numbers by ordered Banach space. After that, various authors proved and extend many fixed point and CFP (common fixed point) results to this space with normal and non-normal cone conditions (see, e.g., [3,6,8,9,11,12,13,14,16,17,18,19]).…”

Section: Introductionmentioning

confidence: 95%

Common Fixed Point Theorem for Compatible Mappings of Type (P) in Multiplicative Cone Metric Space

Saluja,

Jhade

2023

ijmcr

View full text Add to dashboard Cite

show abstract

“…Later, Rehman and Li [36] extended and improved a "fuzzy cone Banach contraction theorem" and proved some generalized fixed point theorems in FCM spaces. Some more properties and related fixed point results can be found in [37][38][39][40][41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Rational Fuzzy Cone Contractions on Fuzzy Cone Metric Spaces with an Application to Fredholm Integral Equations

Rehman

Aydi

2021

Journal of Function Spaces

Self Cite

View full text Add to dashboard Cite

This paper is aimed at proving some common fixed point theorems for mappings involving generalized rational-type fuzzy cone-contraction conditions in fuzzy cone metric spaces. Some illustrative examples are presented to support our work. Moreover, as an application, we ensure the existence of a common solution of the Fredholm integral equations: μ τ = ∫ 0 τ Γ τ , v , μ v d v and ν τ = ∫ 0 τ Γ τ , v , ν v d v , for all μ ∈ U , v ∈ 0 , η , and 0 < η ∈ ℝ , where U = C 0 , η , ℝ is the space of all ℝ -valued continuous functions on the interval 0 , η and Γ : 0 , η × 0 , η × ℝ ⟶ ℝ .

show abstract

Common Fixed Point Theorems for a Pair of Self-Mappings in Fuzzy Cone Metric Spaces

Abstract: In this paper, we present some common fixed point theorems for a pair of self-mappings in fuzzy cone metric spaces under the generalized fuzzy cone contraction conditions. We extend and improve some recent results given in the literature.

Cited by 6 publications

References 23 publications

Weakly compatible and quasi-contraction results in fuzzy cone metric spaces with application to the Urysohn type integral equations

Weakly compatible and quasi-contraction results in fuzzy cone metric spaces with application to the Urysohn type integral equations

Common Fixed Point Theorem for Compatible Mappings of Type (P) in Multiplicative Cone Metric Space

Rational Fuzzy Cone Contractions on Fuzzy Cone Metric Spaces with an Application to Fredholm Integral Equations

Contact Info

Product

Resources

About