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Search for Zeros of Functionals, Fixed Points, and Mappings Coincidence in Quasi-Metric Spaces

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Abstract

The cascade search principle for zeros of (α, β)-search functionals and consequent fixed point and coincidence theorems are proved for collections of single-valued and set-valued mappings of (b1, b2)-quasimetric spaces. These results are extensions of previous author’s results for metric spaces. In particular, a generalization is obtained for the recent result on coincidences of a covering mapping and a Lipschitz mappings of (b1, b2)-quasimetric spaces.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    T. N. Fomenko

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  1. T. N. Fomenko
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Correspondence to T. N. Fomenko.

Additional information

Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2019, Vol. 74, No. 6, pp. 14–22.

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Fomenko, T.N. Search for Zeros of Functionals, Fixed Points, and Mappings Coincidence in Quasi-Metric Spaces. Moscow Univ. Math. Bull. 74, 227–234 (2019). https://doi.org/10.3103/S0027132219060032

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  • DOI: https://doi.org/10.3103/S0027132219060032

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