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Best proximity points: approximation and optimization in partially ordered metric spaces

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Abstract

The purpose of this article is to provide the existence of a unique best proximity point for non-self-mappings by using altering distance function in the setting of partially ordered set which is endowed with a metric. Further, our result provides an extension of a result due to Harjani and Sadarangani to the case of non-self-mappings.

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References

  1. Tarski A.: A lattice-theoretical fixpoint theorem and its applications. Pacif. J. Math. 5, 285–309 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ran A.C.M., Reurings M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132, 1435–1443 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Nieto J.J., Rodríguez-López R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22, 223–239 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Khan M.S., Swaleh M., Sessa S.: Fixed point theorems by altering distances between the points. Bull. Austral. Math. Soc. 30(1), 1–9 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  5. Harjani J., Sadarangani K.: Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations. Nonlinear Anal. 72, 1188–1197 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fan K.: Extensions of two fixed point theorems of F.E. Browder. Math. Z. 122, 234–240 (1969)

    Article  Google Scholar 

  7. De la Sen M., Agarwal R.P.: Some fixed point-type results for a class of extended cyclic self-mappings with a more general contractive condition. Fixed Point Theory Appl. 2011, 59 (2011)

    Article  Google Scholar 

  8. Srinivasan P.S., Veeramani P.: On existence of equilibrium pair for constrained generalized games. Fixed Point Theory Appl. 1, 21–29 (2004)

    MathSciNet  Google Scholar 

  9. Anthony Eldred A., Veeramani P.: Existence and convergence of best proximity points. J. Math. Anal. Appl. 323, 1001–1006 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Al-Thagafi M.A., Shahzad N.: Convergence and existence results for best proximity points. Nonlinear Anal. 70, 3665–3671 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Sadiq Basha S., Veeramani P.: Best proximity pair theorems for multifunctions with open fibres. J. Approx. Theory. 103, 119–129 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kim W.K., Lee K.H.: Existence of best proximity pairs and equilibrium pairs. J. Math. Anal. Appl. 316(2), 433–446 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kirk W.A., Reich S., Veeramani P.: Proximinal retracts and best proximity pair theorems. Numer. Funct. Anal. Optim. 24, 851–862 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Sankar Raj V.: A best proximity point theorem for weakly contractive non-self-mappings. Nonlinear Anal. 74, 4804–4808 (2011)

    Article  MathSciNet  Google Scholar 

  15. Sadiq Basha, S.: Discrete optimization in partially ordered sets. J. Glob. Optim. doi:10.1007/s10898-011-9774-2 (2011)

  16. Abkar A., Gabeleh M.: Best proximity points for cyclic mappings in ordered metric spaces. J. Optim. Theory Appl. 150(1), 188–193 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Abkar, A., Gabeleh, M.: Generalized cyclic contractions in partially ordered metric spaces. Optim. Lett. doi:10.1007/s11590-011-0379-y (2011)

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Authors and Affiliations

  1. Department of Mathematics, Bharathidasan University, Tiruchirappalli, 620 024, Tamil Nadu, India

    V. Pragadeeswarar & M. Marudai

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  1. V. Pragadeeswarar
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  2. M. Marudai
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Correspondence to V. Pragadeeswarar.

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Pragadeeswarar, V., Marudai, M. Best proximity points: approximation and optimization in partially ordered metric spaces. Optim Lett 7, 1883–1892 (2013). https://doi.org/10.1007/s11590-012-0529-x

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  • DOI: https://doi.org/10.1007/s11590-012-0529-x

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