On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems

Meng, Qing

doi:10.1007/s11401-019-0142-8

Cited by 4 publications

(2 citation statements)

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“…They proved some fixed point theorems of contractive mappings on cone metric spaces. Despite all of these studies on cone metric spaces [15][16][17][18][19][20], and Meng and Cho studying algebraic cone metric spaces [21,22], there is much work concerning b-cone metric spaces, for instance, [23][24][25] Hence, by utilizing the concepts in [9,10], this study presents a generalization that represents type I composed cone metric spaces and type II composed cone metric spaces. The examples are for type I composed cone metric space, not cone metric space, and type II composed cone metric space, not for type I composed cone metric space.…”

Section: Introductionmentioning

confidence: 99%

Fredholm integral equation in composed-cone metric spaces

Hijab,

Shaakir,

Aljohani

et al. 2024

Bound Value Probl

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The current paper introduces a novel generalization of cone metric spaces called type I and type II composed cone metric spaces. Therefore, examples of a type I and type II composed cone metric space, which is not a cone metric space, are given. We establish some results of fixed point precisely about Hardy–Rogers type contraction on C2CMS and provide examples. Finally, we present an application of our results and how our results solve the Fredholm integral equation of generalizing several existing and unique fixed point theorems.

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Section: Introductionmentioning

confidence: 99%

Fredholm integral equation in composed-cone metric spaces

Hijab,

Shaakir,

Aljohani

et al. 2024

Bound Value Probl

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“…Recently, Rezapour and Hamlbarani [14] generalized the result of Long-Guang and Xian [11] by omitting the assumption of normality. In 2019, Meng [12] also proved some new "fixed point theorems" concerning generalized algebraic cone metric spaces. Bakr [5] introduces the concept of theta cone metric spaces, and gives further generalizations of some well-known fixed point theorems in 2020.…”

Section: Introductionmentioning

confidence: 99%

Common Fixed Point Theorems of Integral Type Contraction on Cone Metric Spaces and Applications

Kumar,

Singhal,

Sharma

2023

Comm. Math. Appl.

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In this paper, we establish the existence and uniqueness of a common fixed point for two pairs of weakly compatible mappings satisfying integral type contractive condition and property (EA) on cone metric spaces, and we prove the existence and uniqueness of a solution for an ordinary differential equation with periodic boundary conditions. The derived results generalized some wellknown results that exist in the literature.

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