Geodesic
Zero preservation for a family of multivalued functionals, and applications to the theory of fixed points and coincidences
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 13-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theorem on the zero existence preservation for a parametric family of multivalued $(\alpha,\beta)$-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.
Keywords: parametric family of functionals, multivalued mapping, fixed point, coincidence point, Zamfirescu mapping, Zamfirescu-type pair of mappings preservation of coincidence existence, parametric family of mappings. 
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     author = {Yu. N. Zakharyan and T. N. Fomenko},
     title = {Zero preservation for a family of multivalued functionals, and applications to the theory of fixed points and coincidences},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
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Yu. N. Zakharyan; T. N. Fomenko. Zero preservation for a family of multivalued functionals, and applications to the theory of fixed points and coincidences. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 13-17. http://geodesic.mathdoc.fr/item/DANMA_2020_493_a2/

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