Coupled common fixed point results involving "Equation missing" -contractions in ordered generalized metric spaces with application to integral equations

Jain, Manish; Taş, Kenan; Gupta, Namita

doi:10.1186/1029-242x-2013-372

Cited by 3 publications

(4 citation statements)

References 22 publications

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“…We also claim that some results of [6][7][8][9][10]17] can be proved in the case of θ-cone-metric spaces.…”

Section: Definitionmentioning

confidence: 64%

“…is paper gives further generalizations of some well-known coupled fixed-point theorems. Specifically, eorem 3 generalizes the Baskar-Lackshmikantham coupled fixedpoint theorem [3], and eorem 5 generalizes the Sahar Mohamed Ali Abou Bakr fixed-point theorem [4]; the underlying space (E, d θ ) is a complete θ-cone-metric space, and we claim that some results of [6][7][8][9][10] can be proved in the case of θ-cone-metric spaces.…”

Section: Discussionmentioning

confidence: 78%

“…ere are many interesting coupled fixed-point theorems concerning some other type of contraction mappings, see [5][6][7][8][9][10].…”

Section: Definitionmentioning

confidence: 99%

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Coupled Fixed-Point Theorems in Theta-Cone-Metric Spaces

Bakr

2021

Journal of Mathematics

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This paper gives further generalizations of some well-known coupled fixed-point theorems. Specifically, Theorem 3 of the paper is the generalization of the Baskar–Lackshmikantham coupled fixed-point theorem, and Theorem 5 is the generalization of the Sahar Mohamed Ali Abou Bakr fixed-point theorem, where the underlying space is complete θ -cone-metric space.

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“…We also claim that some results of [6][7][8][9][10]17] can be proved in the case of θ-cone-metric spaces.…”

Section: Definitionmentioning

confidence: 64%

Section: Discussionmentioning

confidence: 78%

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Coupled Fixed-Point Theorems in Theta-Cone-Metric Spaces

Bakr

2021

Journal of Mathematics

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“…These results were then extended and generalized by several authors in the last six years (see [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]). Luong and Thuan [26,Theorem 2.1] extended the results of Bhaskar and Lakshmikantham [25] under the following contractive condition:…”

Section: Introductionmentioning

confidence: 85%

Coupled Fixed Point Theorems for (φ,ψ)-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications

Jain¹,

Gupta

Kumar

2014

International Journal of Analysis

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The object of this paper is to establish the existence and uniqueness of coupled fixed points under a (φ, ψ)-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012) and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006), and Luong and Thuan (2011). The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.

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Coupled Fixed Point Results For Mappings Involving (α,ψ) - Weak Contractions In Ordered Metric Spaces And Applications

Jain¹,

Gupta²,

Kumar³

2014

J. Math. Computer Sci.

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In this paper we introduce the notion of , -weak contractions and use the notion to establish the existence and uniqueness of coupled common fixed points for the mixed monotone operators in partially ordered metric spaces. The obtained results extend, improve, complement and unify many recent coupled fixed point results present in the literature. The theoretic results are accompanied with suitable examples. An application to the existence and uniqueness of the solution of the system of integral equations is also presented. 19] proved the following main result. Theorem 1.2 ([19]). Let , ≤ be a partially ordered set and be a metric on such that ( , ) is a complete metric space. Let : × → be a continuous mapping having the mixed monotone property on . Assume that there exists a in [0,1) withthen there exists , in such that = ( , ) and ( , ).In [19, Theorem 2.2], it has also been shown that the continuity assumption of in Theorem 1.2 can be replaced by an alternative condition imposed on convergent non-decreasing and nonincreasing sequences. Assumption 1.1. has the property that (i) if a non-decreasing sequence ⊂ converges to , then ≤ for all , (ii) if a non-increasing sequence ⊂ converges to , then ≥ for all . M. Jain, N. Gupta, S. Kumar / J. Math. Computer Sci. ( ), -25 Berinde [20, Theorem 3], in an alternative way generalized the results of Bhaskar and Lakshmikantham [19] under a weaker contraction given below: , , , + , , , ≤ ( , ) + , , (1.3)with ≥ and ≤ , where ∈ [0,1).On the other hand, Lakshmikantham and C iric [21] extended the notion of mixed monotone property to mixed -monotone property and generalized the results proved in [19] by establishing the existence of coupled coincidence point results using a pair of commutative mappings. This generated new trends in coupled fixed point theory with applications to partially ordered sets. Since then much work has been done in this direction by different authors. For more details the reader may consult ([22-38]). Definition 1. 3 ([21]). Let ( , ≤) be a partially ordered set and : × → and : × → . We say has the mixed -monotone property if is monotone -nondecreasing in its first argument and is monotone -nonincreasing in its second argument; that is, for any

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Coupled common fixed point results involving "Equation missing" -contractions in ordered generalized metric spaces with application to integral equations

Cited by 3 publications

References 22 publications

Coupled Fixed-Point Theorems in Theta-Cone-Metric Spaces

Coupled Fixed-Point Theorems in Theta-Cone-Metric Spaces

Coupled Fixed Point Theorems for (φ,ψ)-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications

Coupled Fixed Point Results For Mappings Involving (α,ψ) - Weak Contractions In Ordered Metric Spaces And Applications

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