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This article is cited in 5 scientific papers (total in 5 papers)
Preservation of the Existence of Zeros in a Family of Set-Valued Functionals and Some Consequences
Yu. N. Zakharyan, T. N. Fomenko Lomonosov Moscow State University
Abstract:
A theorem on the preservation of the existence of zeros under the change of the parameter in a one-parameter family of $(\alpha,\beta)$-search functionals on an open subset of a metric space is proved. The following corollaries of this theorem are presented: on the preservation of the existence of preimages of a given closed subspace in a parametric family of multivalued mappings of metric spaces; on the preservation of the existence of coincidence points in a finite collection of two or more families of multivalued mappings of metric spaces; on the preservation of the existence of common fixed points in a collection of families of multivalued mappings to itself of a metric space. As a simple particular case, the Frigon–Granas theorem (1994) on fixed points of a contraction family of multivalued mappings is obtained.
Keywords:
search functional, family of set-valued functionals, fixed point, coincidence point, contraction family of mappings.
Received: 07.05.2020
Citation:
Yu. N. Zakharyan, T. N. Fomenko, “Preservation of the Existence of Zeros in a Family of Set-Valued Functionals and Some Consequences”, Mat. Zametki, 108:6 (2020), 837–850; Math. Notes, 108:6 (2020), 802–813
Linking options:
https://www.mathnet.ru/eng/mzm12932https://doi.org/10.4213/mzm12932 https://www.mathnet.ru/eng/mzm/v108/i6/p837
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Abstract page: | 239 | Full-text PDF : | 30 | References: | 32 | First page: | 12 |
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