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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 5, Pages 79–96 (Mi izv603)  

This article is cited in 5 scientific papers (total in 5 papers)

On the fixed points of monotonic operators in the critical case

N. B. Engibaryan

Institute of Mathematics, National Academy of Sciences of Armenia

Abstract: We consider the problem of constructing positive fixed points $x$ of monotonic operators $\varphi$ acting on a cone $K$ in a Banach space $E$. We assume that $\|\varphi x\|\le\|x\|+\gamma$, $\gamma>0$, for all $x\in K$. In the case when $\varphi$ has a so-called non-trivial dissipation functional we construct a solution in an extension of $E$, which is a Banach space or a Fréchet space. We consider examples in which we prove the solubility of a conservative integral equation on the half-line with a sum-difference kernel, and of a non-linear integral equation of Urysohn type in the critical case.

DOI: https://doi.org/10.4213/im603

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English version:
Izvestiya: Mathematics, 2006, 70:5, 931–947

Bibliographic databases:

UDC: 517.5
MSC: 45P05, 45B05, 47G10
Received: 11.05.2005
Revised: 12.01.2006

Citation: N. B. Engibaryan, “On the fixed points of monotonic operators in the critical case”, Izv. RAN. Ser. Mat., 70:5 (2006), 79–96; Izv. Math., 70:5 (2006), 931–947

Citation in format AMSBIB
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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. Yengibaryan N.B., Barseghyan A.G., “Semiconservative systems of integral equations with two kernels”, Int. J. Math. Math. Sci., 2011 (2011), 917951, 11 pp.  crossref  mathscinet  zmath  scopus
    2. E. Yu. Elenskaya, “The existence of fixed points of left-continuous monotone operators in spaces with a regular cone”, Russian Math. (Iz. VUZ), 55:10 (2011), 34–40  mathnet  crossref  mathscinet  elib
    3. A. G. Barseghyan, “Integral equations with substochastic kernels”, Eurasian Math. J., 5:4 (2014), 25–32  mathnet
    4. N. B. Engibaryan, “Diskretnaya model nelineinykh zadach perenosa izlucheniya. Printsip invariantnosti i faktorizatsiya”, Matem. modelirovanie, 27:5 (2015), 127–136  mathnet  elib
    5. Kh. A. Khachatryan, “On the solvability of one class of two-dimensional Urysohn integral equations”, Siberian Adv. Math., 28:3 (2018), 166–174  mathnet  crossref  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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