6533b820fe1ef96bd127a669
RESEARCH PRODUCT
Best Proximity Points for Some Classes of Proximal Contractions
Francesca VetroMaryam A AlghamdiNaseer Shahzadsubject
Mathematical optimizationmetric spacesArticle SubjectIterative methodApplied Mathematicslcsh:MathematicsWork (physics)proximal contractionbest proximity pointExtension (predicate logic)Resolution (logic)lcsh:QA1-939Nonlinear programmingReal-valued functionPoint (geometry)Settore MAT/03 - GeometriaContraction principleAnalysisMathematicsdescription
Given a self-mapping g: A → A and a non-self-mapping T: A → B, the aim of this work is to provide sufficient conditions for the existence of a unique point x ∈ A, called g-best proximity point, which satisfies d g x, T x = d A, B. In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x → d g x, T x, thereby getting an optimal approximate solution to the equation T x = g x. An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-self-mappings. © 2013 Maryam A. Alghamdi et al.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-01-01 | Abstract and Applied Analysis |