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

  • Hakan Sahin
  • Mustafa Aslantas
  • Ishak AltunEmail author


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.


Best proximity point multivalued mappings complete metric space 

Mathematics Subject Classification

Primary 54H25 Secondary, 47H10 



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


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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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