Search results for "Cyclic contraction"

showing 5 items of 5 documents

Best proximity point theorems for proximal cyclic contractions

2017

The purpose of this article is to compute a global minimizer of the function $$x\longrightarrow d(x, Tx)$$ , where T is a proximal cyclic contraction in the framework of a best proximally complete space, thereby ensuring the existence of an optimal approximate solution, called a best proximity point, to the equation $$Tx=x$$ when T is not necessarily a self-mapping.

021103 operations researchProximal cyclic contractionApplied Mathematics010102 general mathematicsMathematical analysisBest proximity point0211 other engineering and technologies02 engineering and technologyFunction (mathematics)Fixed pointTopology01 natural sciencesComplete metric spaceCyclic contractionSettore MAT/05 - Analisi MatematicaModeling and SimulationPoint (geometry)Global minimizationGeometry and Topology0101 mathematicsApproximate solutionMathematics
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The existence of best proximity points in metric spaces with the property UC

2009

Abstract Eldred and Veeramani in [A.A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001–1006. MR2260159] proved a theorem which ensures the existence of a best proximity point of cyclic contractions in the framework of uniformly convex Banach spaces. In this paper we introduce a notion of the property UC and extend the Eldred and Veeramani theorem to metric spaces with the property UC.

Discrete mathematicsProperty (philosophy)Applied MathematicsMathematical analysisBest proximity pointBanach spaceRegular polygonMetric spaceCyclic contractionSettore MAT/05 - Analisi MatematicaConvergence (routing)Point (geometry)Property UCAnalysisMathematics
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Best proximity points: Convergence and existence theorems for p-cyclic mappings

2010

Abstract We introduce a new class of mappings, called p -cyclic φ -contractions, which contains the p -cyclic contraction mappings as a subclass. Then, convergence and existence results of best proximity points for p -cyclic φ -contraction mappings are obtained. Moreover, we prove results of the existence of best proximity points in a reflexive Banach space. These results are generalizations of the results of Al-Thagafi and Shahzad (2009) [8] .

Discrete mathematicsPure mathematicsCyclic contractionSettore MAT/05 - Analisi MatematicaApplied Mathematicsp-cyclic contraction mappings p-cyclic \phi-contraction mappings best proximity points reflexive Banach spacesBanach spaceExistence theoremAnalysisMathematics
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Best proximity points for cyclic Meir–Keeler contractions

2008

Abstract We introduce a notion of cyclic Meir–Keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic Meir–Keeler contractions. This theorem is a generalization of a recent result due to Eldred and Veeramani.

Pure mathematicsGeneralizationApplied MathematicsBest proximity pointMathematics::General TopologyExistence theoremCyclic contractionCyclic Meir–Keeler contractionProximal contractionCyclic contractionSettore MAT/05 - Analisi MatematicaCalculusPoint (geometry)UniquenessAnalysisMathematics
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Generalized (varphi,psi)-weak contractions involving (f,g)-reciprocally continuous maps in fuzzy metric spaces

2013

We introduce the notion of (f,g)-reciprocal continuity in fuzzy metric spaces and prove a common fixed point theorem for a pair of sub-compatible maps by employing a generalized (varphi,psi)-weak contraction. As an application of our result, we prove a theorem for a (varphi,psi)-weak cyclic contraction in fuzzy metric spaces.

Settore MAT/05 - Analisi MatematicaCommon fixed point cyclic contraction reciprocally continuous maps sub-compatible maps.
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