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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 5, Pages 239–248 (Mi izv8284)  

This article is cited in 3 scientific papers (total in 3 papers)

Browder functions and theorems on fixed points and coincidences

T. N. Fomenko

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: We introduce the notion of a functional subject to a function series, the notion of a Browder function, and also the notion of a functional subject to a Browder function. We prove theorems on the search for zeros of these functionals. On the basis of this, we obtain a development, for set-valued maps, of Browder's well-known fixed-point theorem and also prove theorems on common pre-images and coincidences of maps of metric spaces which generalize some known results.

Keywords: Browder's theorem, Browder function, search for zeros of a functional, fixed point, coincidence point.

DOI: https://doi.org/10.4213/im8284

Full text: PDF file (400 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:5, 1087–1095

Bibliographic databases:

UDC: 515.124+515.126.4+517.938.5
MSC: Primary 47H10; Secondary 40A05, 49M25, 54H25, 55M20
Received: 14.08.2014

Citation: T. N. Fomenko, “Browder functions and theorems on fixed points and coincidences”, Izv. RAN. Ser. Mat., 79:5 (2015), 239–248; Izv. Math., 79:5 (2015), 1087–1095

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/izv8284
  • https://doi.org/10.4213/im8284
  • http://mi.mathnet.ru/eng/izv/v79/i5/p239

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. T. N. Fomenko, “Fixed points and coincidences of families of mappings between ordered sets and some metrical consequences”, Izv. Math., 83:1 (2019), 151–172  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. T. Fomenko, D. Podoprikhin, “On preservation of common fixed points and coincidences under a homotopy of mapping families of ordered sets”, J. Optim. Theory Appl., 180:1, SI (2019), 34–47  crossref  mathscinet  zmath  isi
    3. T. N. Fomenko, K. S. Yastrebov, “Method for searching zeros of functionals in a conical metric space and questions of its stability”, Moscow University Mathematics Bulletin volume, 75:2 (2020), 58–64  mathnet  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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