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On stationary points of multivalued strongly contractive mappings in partially ordered ultrametric spaces and non-Archimedean

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Abstract

The purpose of this paper is to present a fixed point theorem for multivalued strongly contractive mappings in partially ordered ultrametric spaces. Also a consequence is obtained for these mappings in partially ordered non-Archimedean normed spaces. Finally, two supporting examples of these results are given.

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References

  1. S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales,” Fund. Math. 3, 133–181 (1922).

    MATH  Google Scholar 

  2. I. Beg, A. R. Butt and S. Radojević, “The contraction principle for setvalued mappings on ametric space with a graph,” Comput. Math. Appl. 60 (5), 1214–1219 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  3. I. Beg and H. K. Nashine, “End-point results for multivalued mappings in partially ordered metric spaces,” Int. J. Math. Math. Sci. ID 580250, pp. 19 (2012).

    Google Scholar 

  4. P. Z. Daffer, “Fixed points of generalized contractive multivalued mappings,” J. Math. Anal. Appl. 192, 655–666 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  5. Y. Feng and S. Liu, “Fixed point theorems for multivalued contractive mappings and multivaled Caristi type mappings,” J. Math. Anal. Appl. 317, 103–112 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  6. L. Gajić, “A multivalued fixed point theorem in ultrametric spaces,” Math. Vesnik 54 (3-4), 89–91 (2002).

    MathSciNet  MATH  Google Scholar 

  7. P. Hitzler and A. Seda, “The fixed point theorems of Priess-Crampe and Ribenboim in logic programming,” Valuation Theory and its Applications, Vol. I (Saskatoon, SK, 1999), Fields Inst. Commun. 32, 219–235 (AMS, Providence, RI, 2002.

    Google Scholar 

  8. P. Hitzler and A. Seda, “Multivalued mappings, fixed point theorems and disjunctive data bases,” in Third Irish Workshop on FormalMethods in Computing, British Comp. Soc., pp. 18 (1999).

    Google Scholar 

  9. W. A. Kirk and N. Shahzad, “Some fixed point results in ultrametric spaces,” Topol. Appl. 159 (15), 3327–3334 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  10. D. Klim and D. Wardowski, “Fixed point theorems for multivalued contractions in complete metric spaces,” J. Math. Anal. Appl. 334, 132–139 (1) (2007).

    Article  MathSciNet  MATH  Google Scholar 

  11. S. B. Nadler, “Multivalued contraction mappings,” Pacific J. Math. 30, 475–488 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  12. J. J. Nieto, R. L. Pouso and R. Rodrıguez-López, “Fixed point theorems in ordered abstract spaces,” Proc. Amer. Math. Soc. 135 (8), 2505–2517 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  13. J. J. Nieto and R. Rodrıguez-López, “Contractive mapping theorms in partially ordered sets and applications to ordinary differential equations,” Order 22, 223–239 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  14. D. O’Regan and A. Petruşel, “Fixed point theorems for generalized contractions in ordered metric spaces,” J. Math. Anal. Appl. 341 (2), 1241–1252 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  15. C. Petalas and T. Vidalis, “A fixed point theorem in Non-Archimedean vector spacs,” Amer. Math. Soc. 118 (3), 819–821 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  16. S. Priess-Crampe, “Fixed points and stable balls in ultrametric spaces,” Result. Math. 43, 163–167 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  17. S. Priess-Crampe and P. Ribenboim, “Differential equations over valued fields (and more),” J. Reine Angew. Math. 576, 123–147 (2004).

    MathSciNet  MATH  Google Scholar 

  18. S. Priess-Crampe and P. Ribenboim, “Systems of differential equations over valued fields,” Contemp. Math. 319, 299–318 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  19. S. Priess-Crampe and P. Ribenboim, “The common point theorem for ultrametric spaces,” Geom. Ded. 72, 105–110 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  20. A. C. M. Ran and M. C. B. Reurings, “A fixed point theorm in partially ordered sets and some applications to matrix equations,” Proc. Amer. Math. Soc. 132, 1435–1443 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  21. P. Ribenboim, “Fermatś equation for matrices or quaternions over q-adic fields,” Acta Arith. 113, 241–250 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  22. A. Tarski, “A lattice theoretical fixed point and its application,” Pacific J. Math. 5, 285–309 (1955).

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Van der Hoeven, Transseries and Real Differential Algebra, Lecture Notes in Mathematics (Springer-Verlag, Berlin, 2006).

    Book  MATH  Google Scholar 

  24. A. C. M. Van Rooij, Non-Archimedean Functional Analysis (Marcel Dekker, 1978).

    MATH  Google Scholar 

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Correspondence to Hamid Mamghaderi.

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Mamghaderi, H., Masiha, H.P. On stationary points of multivalued strongly contractive mappings in partially ordered ultrametric spaces and non-Archimedean. P-Adic Num Ultrametr Anal Appl 9, 144–150 (2017). https://doi.org/10.1134/S2070046617020042

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  • DOI: https://doi.org/10.1134/S2070046617020042

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