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Graphical metric space: a generalized setting in fixed point theory

Calogero VetroStojan RadenovićStojan RadenovićSatish Shukla

subject

Pseudometric space01 natural sciencesGraphIntrinsic metricOrdered metric spaceSettore MAT/05 - Analisi MatematicaGraphical metric spaceContraction mapping0101 mathematicsMathematicsDiscrete mathematicsAlgebra and Number TheoryApplied MathematicsInjective metric space010102 general mathematicsFixed pointConvex metric space010101 applied mathematicsAlgebraComputational MathematicsMetric spaceGeometry and TopologySettore MAT/03 - GeometriaMetric differentialAnalysisFisher information metric

description

Building on recent ideas of Jachymski, we work on the notion of graphical metric space and prove an analogous result for the contraction mapping principle. In particular, the triangular inequality is replaced by a weaker one, which is satisfied by only those points which are situated on some path included in the graphical structure associated with the space. Some consequences, examples and an application to integral equations are presented to confirm the significance and unifying power of obtained generalizations.

yearjournalcountryeditionlanguage
2016-07-08
10.1007/s13398-016-0316-0http://hdl.handle.net/10447/235762