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Feng–Liu type approach to best proximity point results for multivalued mappings

  • Hakan Sahin
  • Mustafa Aslantas
  • Ishak AltunEmail author
Article
  • 79 Downloads

Abstract

Let (Xd) be a metric space, A and B be two nonempty subsets of X,  and \(T:A\rightarrow B\) be a mapping. In this case, since the equation \(x=Tx\) may not have an exact solution, it is meaningful to explore the approximate solution. The best approximation results in the literature are related to investigate such solutions. Further, best proximity point theorems not only investigate the approximate solution of the equation \(x=Tx,\) but also an optimal solution of the minimization problem \(\min \{d(x,Tx):x\in A\}\). Such points are called the best proximity points of the mapping T. In this paper, considering the Feng and Liu’s approach in fixed point theory, we present some new results for best proximity points of nonself multivalued mappings.

Keywords

Best proximity point multivalued mappings complete metric space 

Mathematics Subject Classification

Primary 54H25 Secondary, 47H10 

Notes

Acknowledgements

The authors are thankful to the referee for making valuable suggestions leading to a better presentation of the paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and ArtsAmasya UniversityAmasyaTurkey
  2. 2.Department of Mathematics, Faculty of ScienceÇankırı Karatekin UniversityÇankırıTurkey
  3. 3.Department of Mathematics, Faculty of Science and ArtsKırıkkale UniversityYahsihan KirikkaleTurkey

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