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A common fixed point theorem for pairs of non-self mappings in a length space

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Abstract

Using the technique of altering distances, we establish a common fixed point theorem for two pairs of non-self mappings in the framework of length spaces.

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References

  1. Asad, A.J., and Z. Ahmad. 1999. Common fixed point of a pair of mappings in Banach spaces. Southeast Asian Bulletin of Mathematics 23: 349–355.

    MathSciNet  Google Scholar 

  2. Assad, N.A., and W.A. Kirk. 1972. Fixed point theorems for set-valued mappings of contractive type. Pacific Journal of Mathematics 43: 553–562.

    Article  MathSciNet  Google Scholar 

  3. Assad, N.A. 1976. On a fixed point theorem of Kannan in Banach spaces. Tamkang Journal of Mathematics 7: 91–94.

    MathSciNet  Google Scholar 

  4. Assad, N.A. 1988. On some nonself nonlinear contractions. Mathematics Japon 33 (1): 17–26.

    MathSciNet  Google Scholar 

  5. Burago, D., Y. Burago, and S. Ivanov. 2001. A course in metric geometry, graduate studies in mathematics, 33. Providence, RI: American Mathematical Society.

    Google Scholar 

  6. Ćirić, L., V. Rakočević, S. Radenović, M. Rajović, and R. Lazović. 2010. Common fixed point theorems for nonself mappings in metric spaces of hyperbolic type. Journal of Computational and Applied Mathematics 233: 2966–2974.

    Article  ADS  MathSciNet  Google Scholar 

  7. Hadzić, O., and L. Gajic. 1986. Coincidence points for set-valued mappings in convex metric spaces. Univ u Novom Sadu Zb Rad Prirod Mat Fak Ser Mat 16 (1): 13–25.

    MathSciNet  Google Scholar 

  8. Imdad, M., and J. Ali. 2009. Reciprocal continuity and common fixed points of nonself mappings. Taiwanese Journal of Mathematics 13 (5): 1457–1473.

    Article  MathSciNet  Google Scholar 

  9. Imdad, M., and L. Khan. 2005. Common fixed point theorems for nonself mappings in metrically convex spaces via altering distances. International Journal of Mathematics and Mathematical Sciences 24: 4029–4039.

    Article  Google Scholar 

  10. Imdad, M., and L. Khan. 2007. Some common fixed point theorems for a family of mappings in metrically convex spaces. Nonlinear Analysis 67: 2717–2726.

    Article  MathSciNet  Google Scholar 

  11. Imdad, M., and S. Kumar. 2003. Rhoades type fixed point theorems for a pair of nonself mappings. Computers and Mathematics with Applications 46: 919–927.

    Article  MathSciNet  Google Scholar 

  12. Jungck, G. 1986. compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences 9 (4): 771–779.

    Article  MathSciNet  Google Scholar 

  13. Jungck, G., and B.E. Rhoades. 1998. Fixed points for set-valued functions without continuity. Indian Journal of Pure and Applied Mathematics 29 (3): 227–238.

    MathSciNet  Google Scholar 

  14. Khan, M.S., M. Swaleh, and S. Sessa. 1984. Fixed point theorems by altering distances between the points. Bulletin of the Australian Mathematical Society 30: 1–9.

    Article  MathSciNet  Google Scholar 

  15. Khan, M.S., H.K. Pathak, and M.D. Khan. 2000. Some fixed point theorems in metrically convex spaces. Georgian Mathematical Journal 7 (3): 523–530.

    Article  MathSciNet  Google Scholar 

  16. Lang, U. 2013. Length spaces, preprint

  17. Menger, K. 1928. Untersuchungen über allgemeine Metrik. Math. Ann. 100 (1), 75–163.

  18. Oyewole, O.K., S. Reich, and A.J. Zaslavski. 2022. A fixed point theorem in length spaces. Dynamic Systems and Applications 31 (3): 173–180.

    Article  Google Scholar 

  19. Papadopoulos, A. 2014. Metric spaces, convexity and nonpositive curvature, 2nd ed. Zürich: European Mathematical Society.

    Book  Google Scholar 

  20. Park, S. 1980. A unified approach to fixed points of contractive maps. Journal of the Korean Mathematical Society 16 (2): 95–105.

    MathSciNet  Google Scholar 

  21. Pathak, H.K., and R. Sharma. 1994. A note on fixed point theorems of Khan, Swaleh and Sessa. Mathematical Edition (Siwan) 28 (3): 151–157.

    MathSciNet  Google Scholar 

  22. Reich, S. 1972. Fixed points in locally convex spaces. Mathematische Zeitschrift 125: 17–31.

    Article  MathSciNet  Google Scholar 

  23. Reich, S. 1973. Fixed points of condesing functions. Journal of Mathematical Analysis and Applications 41: 460–467.

    Article  MathSciNet  Google Scholar 

  24. Reich, S. 1976. On fixed point theorems obtained from existence theorems for differential rquations. Journal of Mathematical Analysis and Applications 54: 26–36.

    Article  MathSciNet  Google Scholar 

  25. Reich, S. 1978. Approximate selections, best approximations, fixed points, and invariant sets. Journal of Mathematical Analysis and Applications 62: 104–113.

    Article  MathSciNet  Google Scholar 

  26. Rhoades, B.E. 1978. A fixed point theorem for some nonself mappings. Mathematics Japon 23 (4): 457–459.

    Google Scholar 

  27. Sastry, K.P.R., and G.V.R. Babu. 1999. Some fixed point theorems by altering distances between the points. Indian Journal of Pure and Applied Mathematics 30 (6): 641–647.

    MathSciNet  Google Scholar 

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Acknowledgements

The authors are grateful to an anonymous referee for his/her pertinent and helpful comments and suggestions.

Funding

Simeon Reich was partially supported by the Israel Science Foundation (Grant No. 820/17), by the Fund for the Promotion of Research at the Technion (Grant 2001893) and by the Technion General Research Fund (Grant 2016723).

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Authors and Affiliations

  1. Department of Mathematics, The Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Olawale K. Oyewole, Simeon Reich, Adeolu Taiwo & Alexander J. Zaslavski

Authors
  1. Olawale K. Oyewole
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  2. Simeon Reich
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  3. Adeolu Taiwo
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  4. Alexander J. Zaslavski
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Contributions

All authors worked equally on the results and approved the final manuscript.

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Correspondence to Olawale K. Oyewole.

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Communicated by S Ponnusamy.

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Oyewole, O.K., Reich, S., Taiwo, A. et al. A common fixed point theorem for pairs of non-self mappings in a length space. J Anal 32, 669–680 (2024). https://doi.org/10.1007/s41478-023-00644-w

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  • DOI: https://doi.org/10.1007/s41478-023-00644-w

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