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Zero Preservation for a Family of Multivalued Functionals, and Applications to the Theory of Fixed Points and Coincidences

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Abstract

A theorem on the zero existence preservation for a parametric family of multivalued (α, β)-search functionals on an open subset of a metric space is proved. Several corollaries on the existence preservation for preimages of a closed subspace, for coincidence points, and for common fixed points under the action of a parametric family (a number of families) of mappings are obtained. The notion of a Zamfirescu-type pair of mappings is introduced, and a coincidence theorem for such pairs of mappings is obtained. In addition, a theorem on the coincidence existence preservation for a parametric family of such pairs of mappings is obtained. The obtained results imply several well-known theorems.

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Funding

This work was performed within the research directions of the Moscow Center of Fundamental and Applied Mathematics.

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Authors and Affiliations

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

    T. N. Fomenko

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991, 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.

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Translated by I. Ruzanova

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Fomenko, T.N., Zakharyan, Y.N. 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

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  • DOI: https://doi.org/10.1134/S1064562420040225

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