Generalized contractions in partially ordered metric spaces

doi:10.1080/00036810701556151

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Generalized contractions in partially ordered metric spaces

Journal Article•DOI•

Generalized contractions in partially ordered metric spaces

Ravi P. Agarwal¹, El Gebeily², Donal O'Regan³•Institutions (3)

Florida Institute of Technology¹, King Fahd University of Petroleum and Minerals², National University of Ireland, Galway³

22 Jan 2008-Applicable Analysis (APPLICABLE ANALYSIS)-Vol. 87, Iss: 1, pp 109-116

TL;DR: In this article, the authors present some fixed point results for monotone operators in a metric space endowed with a partial order using a weak generalized contraction-type assumption, which is similar to the one used in this paper.

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Abstract: We present some fixed point results for monotone operators in a metric space endowed with a partial order using a weak generalized contraction-type assumption.

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Journal Article•DOI•

Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces

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V. Lakshmikantham¹, Ljubomir Ćirić²•Institutions (2)

Florida Institute of Technology¹, University of Belgrade²

15 Jun 2009-Nonlinear Analysis-theory Methods & Applications

TL;DR: In this paper, Bhaskar and Lakshmikantham introduced the concept of a mixed g-monotone mapping and proved coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces.

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Abstract: We introduce the concept of a mixed g -monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces. Presented theorems are generalizations of the recent fixed point theorems due to Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379–1393] and include several recent developments.

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799 citations

Journal Article•DOI•

Fixed point theorems for α–ψ-contractive type mappings

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Bessem Samet¹, Calogero Vetro², Pasquale Vetro²•Institutions (2)

Tunis University¹, University of Palermo²

01 Mar 2012-Nonlinear Analysis-theory Methods & Applications

TL;DR: In this paper, the authors introduce a new concept of α - ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces.

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Abstract: In this paper, we introduce a new concept of α – ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.

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749 citations

Journal Article•DOI•

Fixed point theorems for weakly contractive mappings in partially ordered sets

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J. Harjani¹, Kishin Sadarangani¹•Institutions (1)

University of Las Palmas de Gran Canaria¹

01 Oct 2009-Nonlinear Analysis-theory Methods & Applications

TL;DR: In this paper, the authors present fixed point theorems for weakly contractive maps in a complete metric space endowed with a partial order, and present a generalization of the fixed point theorem.

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Abstract: The purpose of this paper is to present some fixed point theorems for weakly contractive maps in a complete metric space endowed with a partial order.

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341 citations

Journal Article•DOI•

Fixed point theorems for generalized contractions in ordered metric spaces

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Donal O'Regan¹, Adrian Petruşel²•Institutions (2)

National University of Ireland, Galway¹, Babeș-Bolyai University²

15 May 2008-Journal of Mathematical Analysis and Applications

TL;DR: In this article, Nieto et al. present fixed point results for self-generalized contractions in ordered metric spaces, which generalize and extend some recent results of A.C. Reurings.

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327 citations

Journal Article•DOI•

Generalized - Contractive Type Mappings and Related Fixed Point Theorems with Applications

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Erdal Karapınar¹, Bessem Samet²•Institutions (2)

Atılım University¹, King Saud University²

02 Sep 2012-Abstract and Applied Analysis

TL;DR: In this paper, fixed point theorems for cyclic contractive mappings are established for metric spaces endowed with a partial order and for a class of contractive mapping mappings.

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Abstract: We establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.

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290 citations

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Journal Article•DOI•

A fixed point theorem in partially ordered sets and some applications to matrix equations

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André C. M. Ran¹, Martine C.B. Reurings¹•Institutions (1)

VU University Amsterdam¹

18 Sep 2003

TL;DR: In this paper, an analogue of Banach's fixed point theorem in partially ordered sets is proved, and several applications to linear and nonlinear matrix equations are discussed, including the application of the Banach theorem to the Partially ordered Set (POPS) problem.

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Abstract: An analogue of Banach's fixed point theorem in partially ordered sets is proved in this paper, and several applications to linear and nonlinear matrix equations are discussed.

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1,323 citations

"Generalized contractions in partial..." refers background or methods or result in this paper

...This approach was initiated in [2] and the results in [1] are slight extensions of those in [2]....
[...]
...This article presents new results for generalized contractions in partially ordered metric spaces (we note that the results in [1,2] follow from ours by taking (t)1⁄4 k t)....
[...]
...Recently in [1,2] the Banach contraction principle was discussed in a metric space endowed with a partial order....
[...]
...The main idea in [1,2] involve combining the ideas in the contraction principle with those in the monotone iterative technique....
[...]

Journal Article•DOI•

Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations

[...]

Juan J. Nieto¹, Rosana Rodríguez-López¹•Institutions (1)

University of Santiago de Compostela¹

22 Nov 2005-Order

TL;DR: It is proved the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a lower solution.

...read moreread less

Abstract: We prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a lower solution. To this aim, we prove an appropriate fixed point theorem in partially ordered sets.

...read moreread less

1,159 citations

"Generalized contractions in partial..." refers background or methods or result in this paper

...This approach was initiated in [2] and the results in [1] are slight extensions of those in [2]....
[...]
...This article presents new results for generalized contractions in partially ordered metric spaces (we note that the results in [1,2] follow from ours by taking (t)1⁄4 k t)....
[...]
...Recently in [1,2] the Banach contraction principle was discussed in a metric space endowed with a partial order....
[...]
...The main idea in [1,2] involve combining the ideas in the contraction principle with those in the monotone iterative technique....
[...]

Journal Article•DOI•

Random and deterministic fixed point theory for generalized contractive maps

[...]

Ravi P. Agarwal¹, Donal O'Regan², M. Sambandham³•Institutions (3)

Florida Institute of Technology¹, National University of Ireland, Galway², Morehouse College³

01 Jul 2004-Applicable Analysis

TL;DR: In this paper, fixed point and homotopy results for generalized contractions on complete gauge spaces were obtained for generalized generalized contracts, and random fixed point results were given for generalized contracts on complete-gauge spaces.

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Abstract: Fixed point and homotopy results are presented for generalized contractions on complete gauge spaces. In addition we obtain random fixed point results for generalized contractions.

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18 citations