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On Coincidence Points for a Zamfirescu Type Pair of Multi-Valued Mappings

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Abstract

A concept of a Zamfirescu type pair of multi-valued mappings between metric spaces is introduced. A coincidence existence theorem is proved for such pairs of mappings. It is shown that the result is a generalization of the main result of the recent joint work by K. Neammanee and A. Kaevkhao, in which the concept of a multi-valued Zamfirescu mapping was introduced and the fixed point existence and approximation theorems were proved. In addition, it is shown in this paper that all listed results are special cases of the principle of search for zeros of special \((1,\lambda)\)-search functionals proposed earlier by T. N. Fomenko.

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REFERENCES

  1. T. Zamfirescu, ‘‘Fixed point theorems in metric spaces,’’ Arch. Math. (Basel) 23, 292–298 (1972).

    Article  MathSciNet  Google Scholar 

  2. S. Banach, ‘‘Sur les operations dans les ensembles abstraits et leur application aux equations integrales,’’ Fund. Math. 3, 133–181 (1922). https://doi.org/10.4064/fm-3-1-133-181 

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Kannan, ‘‘Some results on fixed points,’’ Bull. Calcutta Math. Soc. 10, 71–76 (1968).

    MathSciNet  MATH  Google Scholar 

  4. S. K. Chatterjea, ‘‘Fixed-point theorems,’’ C. R. Acad. Bulgare Sci. 25, 727–730 (1972).

    MathSciNet  MATH  Google Scholar 

  5. S. B. Nadler, ‘‘Multi-valued contraction mappings,’’ Not. Am. Math. Soc. 14, 930 (1967).

    Google Scholar 

  6. S. B. Nadler, ‘‘Multi-valued contraction mappings,’’ Pac. J. Math. 30, 475–488 (1969).

    Article  MathSciNet  Google Scholar 

  7. K. Neammanee and A. Kaevkhao, ‘‘Fixed point theorems of multi-valued Zamfirescu mappings,’’ J. Math. Res. 2 (2), 150–156 (2010).

    Article  Google Scholar 

  8. T. N. Fomenko, ‘‘Approximation of coincidence points and common fixed points of a collection of mappings of metric spaces’’, Math. Notes 86, 107–120 (2009). https://doi.org/10.1134/S0001434609070104 

    Article  MathSciNet  MATH  Google Scholar 

  9. T. N. Fomenko, ‘‘Cascade search of the coincidence set of collections of multivalued mappings,’’ Math. Notes. 86, 276–281 (2009). https://doi.org/10.1134/S0001434609070293 

    Article  MathSciNet  MATH  Google Scholar 

  10. T. N. Fomenko, ‘‘Cascade search principle and its applications to the coincidence problem of \(n\) one-valued or multi-valued mappings,’’ Topol. Its Appl. 157, 760–773 (2010). https://doi.org/10.1016/j.topol.2009.08.006 

    Article  MATH  Google Scholar 

  11. T. N. Fomenko, ‘‘Fixed points and coincidences of families of mappings between ordered sets and some metrical consequences,’’ Izv. Math. 83, 151–172 (2019). doi 10.1070/IM8768

    Article  MathSciNet  MATH  Google Scholar 

  12. T. N. Fomenko, ‘‘Functionals strictly subjected to convergent series and search for singularities of mappings,’’ J. Fixed Point Theory Appl. 14, 21–40 (2013). https://doi.org/10.1007/s11784-014-0155-6

    Article  MathSciNet  MATH  Google Scholar 

  13. T. N. Fomenko and Yu. N. Zakharyan, ‘‘Zero preservation for a family of multivalued functionals, and applications to the theory of fixed points and coincidences,’’ Dokl. Math. 102, 272–275 (2020). https://doi.org/10.1134/S1064562420040225 

    Article  Google Scholar 

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Authors and Affiliations

  1. Chair of General Mathematics, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    T. N. Fomenko

  2. Chair of General Topology and Geometry, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    Yu. N. Zakharyan

Authors
  1. T. N. Fomenko
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  2. Yu. N. Zakharyan
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Corresponding authors

Correspondence to T. N. Fomenko or Yu. N. Zakharyan.

Additional information

Translated by E. Oborin

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Fomenko, T.N., Zakharyan, Y.N. On Coincidence Points for a Zamfirescu Type Pair of Multi-Valued Mappings. Moscow Univ. Math. Bull. 75, 253–260 (2020). https://doi.org/10.3103/S002713222006008X

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  • DOI: https://doi.org/10.3103/S002713222006008X

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