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Existence and uniqueness of best proximity points under rational contractivity conditions

  • Erdal Karapinar , Antonio-Francisco Roldán-López-de-Hierro EMAIL logo and Kishin Sadarangani EMAIL logo
Published/Copyright: December 30, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 6

Abstract

The main aim of this paper is to present some theorems in order to guarantee existence and uniqueness of best proximity points under rational contractivity conditions using very general test functions. To illustrate the variety of possible test functions, we include some examples of pairs of functions which are included in innovative papers published in the last years. As a consequence, we prove that our results unify and extend some recent results in this field.

MSC 2010: Primary 46T99; 47H10; 47H09; 54H25
Keywords: best proximity point; fixed point; rational contractive condition; P-property; weak P-property

The second author has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE

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(Communicated by Gregor Dolinar)

Acknowledgement

The authors thanks to anonymous referees for their remarkable comments, suggestion and ideas that helped to improve this paper.

References

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Received: 2014-1-26
Accepted: 2014-8-21
Published Online: 2016-12-30
Published in Print: 2016-12-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2016-0234
Keywords for this article
best proximity point; fixed point; rational contractive condition; P-property; weak P-property

Articles in the same Issue

  2. A triple representation of lattice effect algebras
  4. Periods of morgan-voyce sequences and elliptic curves
  6. Multiplicative generalized derivations on ideals in semiprime rings
  8. A few remarks on Poincaré-Perron solutions and regularly varying solutions
  10. Applications of extremal theorem and radius equation for a class of analytic functions
  12. On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions
  14. New criteria for global exponential stability of linear time-varying volterra difference equations
  16. On approximation of functions by some hump matrix means of Fourier series
  18. Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras
  20. Poisson kernels on semi-direct products of abelian groups
  22. Locally convex projective limit cones
  24. On the properties (wL) and (wV)
  26. On the existence of solutions for quadratic integral equations in Orlicz spaces
  28. Existence and uniqueness of best proximity points under rational contractivity conditions
  30. Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds
  32. On the internal approach to differential equations 3. Infinitesimal symmetries
  34. A Characterization of the discontinuity point set of strongly separately continuous functions on products
  36. Wick differential and Poisson equations associated to the 𝚀𝚆𝙽-Euler operator acting on generalized operators
  38. Multivariate EIV models
  40. On codes over 𝓡k, m and constructions for new binary self-dual codes
  42. Domination number of total graphs
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