Search results for "optimal approximate solution"

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Best proximity point theorems for rational proximal contractions

2013

Abstract We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results. MSC:41A65, 46B20, 47H10.

Discrete mathematicsPure mathematicsMetric spaceDifferential geometrySettore MAT/05 - Analisi MatematicaApplied MathematicsProximity problemsUniquenessGeometry and TopologyFixed pointPoint theorybest proximity point contraction fixed point generalized proximal contraction optimal approximate solutionMathematicsFixed Point Theory and Applications
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Common best proximity points and global optimal approximate solutions for new types of proximal contractions

2015

Let $(\mathcal{X},d)$ be a metric space, $\mathcal{A}$ and $\mathcal{B}$ be two non-empty subsets of $\mathcal{X}$ and $\mathcal{S},\mathcal{T}: \mathcal{A} \to \mathcal{B}$ be two non-self mappings. In view of the fact that, given any point $x \in \mathcal{A}$, the distances between $x$ and $\mathcal{S}x$ and between $x$ and $\mathcal{T}x$ are at least $d(\mathcal{A}, \mathcal{B}),$ which is the absolute infimum of $d(x, \mathcal{S} x)$ and $d(x, \mathcal{T} x)$, a common best proximity point theorem affirms the global minimum of both the functions $x \to d(x, \mathcal{S}x)$ and $x \to d(x, \mathcal{T}x)$ by imposing the common approximate solution of the equations $\mathcal{S}x = x$ and $…

common best proximity pointproximally commuting mappingsSettore MAT/05 - Analisi Matematicaoptimal approximate solution
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