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Best proximity and remotest points results for weakly strongly lowear map** and weakly strongly upper map**

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Abstract

In this paper, we give new conditions for existence and uniqueness of best proximity and remotest points for weakly strongly lower map** and weakly strongly upper map**.

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References

  1. Ahmadi Baseri, M., and H. Mazaheri. 2017. Best proximity points for semi-cyclic contraction pairs in regular cone metric spaces. Mathematical Sciences and Applications E-Notes 5 (2): 36–44.

    Article  MathSciNet  MATH  Google Scholar 

  2. Ahmadi Baseri, M., and H. Mazaheri. 2018. Remotest points and approximate remotest points in metric spaces. Iranian Journal of Science and Technology, Transactions A: Science 42 (1): 21–24.

    Article  MathSciNet  MATH  Google Scholar 

  3. Ahmadi Baseri, M., H. Mazaheri, B.S. Lee, and T.D. Narang. 2016. Best proximity points theorems for cone generalized cyclic \(\varphi \)-contraction maps in cone metric spaces. Advances and Applications in Mathematical Sciences 15 (6): 161–168.

    MathSciNet  MATH  Google Scholar 

  4. Baronti, M., and P.L. Papini. 2001. Remotal sets revisted. Taiwanese Journal of Mathematics 5: 367–373.

    Article  MathSciNet  MATH  Google Scholar 

  5. Bosznay, A.P. 1979. A remark on the farthest point problem. Journal of Approximation Theory 27: 309–312.

    Article  MathSciNet  MATH  Google Scholar 

  6. Boulos, W., and S. Reich. 2014. Farthest points and porosity. Journal of Nonlinear and Convex Analysis 15: 1319–1329.

    MathSciNet  MATH  Google Scholar 

  7. Boulos, W., and S. Reich. 2015. Porosity results for two-set nearest and farthest point problems. Rendiconti del Circolo Matematico di Palermo 2 (64): 493–507.

    Article  MathSciNet  MATH  Google Scholar 

  8. Deville, R., and V.E. Zizler. 1988. Farthest points in \(w^*\)-compact sets. Bulletin of the Australian Mathematical Society 38: 433–439.

    Article  MathSciNet  MATH  Google Scholar 

  9. Edelstein, M. 1966. Farthest points of sets in uniformly convex Banach spaces. Israel Journal of Mathematics 4: 171–176.

    Article  MathSciNet  MATH  Google Scholar 

  10. Khalil, R., and Sh. Al-Sharif. 2006. Remotal sets in vector valued function spaces. Scientiae Mathematicae Japonicae 3: 433–441.

    MathSciNet  MATH  Google Scholar 

  11. Kirk, W.A., S. Reich, and P. Veeramani. 2003. Proximinal retracts and best proximity pair theorems. Numerical Functional Analysis and Optimization 24: 851–862.

    Article  MathSciNet  MATH  Google Scholar 

  12. Mazaheri, H., and M. Zarenejhad. 2014. Some new results on remotest points in normed spaces. The Journal of Mahani Mathematical Research Center 3 (2): 37–50.

    MATH  Google Scholar 

  13. Mazaheri, H., T.D. Narang, and H.R. Khademzadeh. 2015. Nearest and Farthest points in normed spaces. Yazd: In Press Yazd University.

    Google Scholar 

  14. Narang, T.D. 1977. A study of farthest points. Nieuw Archief voor Wiskunde 25: 54–79.

    MathSciNet  MATH  Google Scholar 

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Correspondence to H. Mazaheri.

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Communicated by S Ponnusamy.

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Mazaheri, H., Gholipour, R. Best proximity and remotest points results for weakly strongly lowear map** and weakly strongly upper map**. J Anal 31, 2575–2585 (2023). https://doi.org/10.1007/s41478-023-00580-9

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  • DOI: https://doi.org/10.1007/s41478-023-00580-9

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