Best Proximity Results with Applications to Nonlinear Dynamical Systems

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ID: 260594
2019
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Abstract
Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution ω that is optimal in the sense that the error σ ( ω , J ω ) assumes the global minimum value σ ( θ , ϑ ) . The aim of this paper is to define the notion of Suzuki α - Θ -proximal multivalued contraction and prove the existence of best proximity points ω satisfying σ ( ω , J ω ) = σ ( θ , ϑ ) , where J is assumed to be continuous or the space M is regular. We derive some best proximity results on a metric space with graphs and ordered metric spaces as consequences. We also provide a non trivial example to support our main results. As applications of our main results, we discuss some variational inequality problems and dynamical programming problems.
Reference Key
al-sulami2019mathematicsbest Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Hamed H Al-Sulami;Nawab Hussain;Jamshaid Ahmad;Al-Sulami, Hamed H;Hussain, Nawab;Ahmad, Jamshaid;
Journal Mathematics
Year 2019
DOI
10.3390/math7100900
URL
https://doi.org/10.3390/math7100900
Keywords
graphs nonlinear dynamical systems best proximity point α-proximal contraction multi-valued mappings

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