Fixed point and common fixed point theorems on ordered cone metric spaces

Altun, İshak; Damjanović, Boško; Djoric, Dragan

doi:10.1016/j.aml.2009.09.016

Cited by 122 publications

(59 citation statements)

References 21 publications

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“…Definition 1.13. ( [7]) Let (X, ) be a partially ordered set. Two mappings f, : X → X are said to be weakly increasing maps, if f x f x and x f x hold for all x ∈ X .…”

Section: Definition 11 ([14])mentioning

confidence: 99%

Existence of common fixed point for b-metric rational type contraction

Abbas

Cheema

Razani

2016

Filomat

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Abstract.The necessary conditions for existence of a common fixed point of two mappings satisfying generalized b-order contractive condition in the setting of a partially ordered b-complete b-metric space are presented. Also, we study well-posedness of common fixed point problem for generalized b-order contractive mappings. We employ our result to establish an existence of a solution of an integral equation.

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“…Definition 1.13. ( [7]) Let (X, ) be a partially ordered set. Two mappings f, : X → X are said to be weakly increasing maps, if f x f x and x f x hold for all x ∈ X .…”

Section: Definition 11 ([14])mentioning

confidence: 99%

Existence of common fixed point for b-metric rational type contraction

Abbas

Cheema

Razani

2016

Filomat

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“…Huang and Zhang [7] re-introduced such spaces under the name of cone metric spaces, and went further, defining convergent and Cauchy sequences in the terms of interior points of the underlying cone. Afterwards, many papers about fixed point theory in cone metric spaces were appeared (see, for example, [8][9][10][11][12][13][14][15]). …”

Section: Introductionmentioning

confidence: 99%

Coupled fixed point results in cone metric spaces for "Equation missing" -compatible mappings

Aydi

Samet

Vetro

2011

Fixed Point Theory Appl

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In this paper, we introduce the concepts of w -compatible mappings, b-coupled coincidence point and b-common coupled fixed point for mappings F, G : X × X X, where (X, d) is a cone metric space. We establish b-coupled coincidence and bcommon coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature, in particular the recent results of Abbas et al. [Appl. Math. Comput. 217, 195-202 (2010)]. Some examples are given to illustrate our obtained results. An application to the study of existence of solutions for a system of non-linear integral equations is also considered.

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“…They greatly expanded the famous Banach contraction principle in such setting. Since then, a lot of papers have appeared on cone metric spaces and b-metric spaces (see [1,5,11,15,21,28,33,35]). Hussain and Shah [20] introduced cone b-metric space and generalized both cone metric space and b-metric space.…”

Section: Introductionmentioning

confidence: 99%

Tripled random coincidence point and common fixed point results of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras

Jiang¹,

Cai²,

Chen³

et al. 2017

J. Nonlinear Sci. Appl.

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In this paper, based on the concept of cone b-metric space over Banach algebra, which was introduced by Huang and Radenovic [H.-P. Huang, S. Radenović, J. Nonlinear Sci. Appl., 8 (2015), 787-799], we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces. We consider the obtained assertions without the assumption of normality of cones. The presented results generalize some coupled common fixed point theorems in the existing literature. c 2017 all rights reserved.Keywords: Tripled random fixed point, tripled random coincidence point, cone b-metric space over Banach algebra, generalized Lipschitz constant, tripled common random fixed point. 2010 MSC: 54H25, 47H10, 54E50.

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Fixed point and common fixed point theorems on ordered cone metric spaces

Cited by 122 publications

References 21 publications

Existence of common fixed point for b-metric rational type contraction

Existence of common fixed point for b-metric rational type contraction

Coupled fixed point results in cone metric spaces for "Equation missing" -compatible mappings

Tripled random coincidence point and common fixed point results of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras

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