Monotone iterative technique and connectedness of the set of solutions

Boris Rudolf

Mathematica Bohemica (2000)

  • Volume: 125, Issue: 3, page 323-329
  • ISSN: 0862-7959

Abstract

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The paper deals with the properties of a monotone operator defined on a subset of an ordered Banach space. The structure of the set of fixed points between the minimal and maximal ones is described.

How to cite

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Rudolf, Boris. "Monotone iterative technique and connectedness of the set of solutions." Mathematica Bohemica 125.3 (2000): 323-329. <http://eudml.org/doc/248664>.

@article{Rudolf2000,
abstract = {The paper deals with the properties of a monotone operator defined on a subset of an ordered Banach space. The structure of the set of fixed points between the minimal and maximal ones is described.},
author = {Rudolf, Boris},
journal = {Mathematica Bohemica},
keywords = {order preserving operator; ordered Banach space; structure of the set of fixed points; fixed points between the minimal and maximal ones; connectedness of the set of solutions; order preserving operator; ordered Banach space; structure of the set of fixed points; fixed points between the minimal and maximal ones; connectedness of the set of solutions},
language = {eng},
number = {3},
pages = {323-329},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Monotone iterative technique and connectedness of the set of solutions},
url = {http://eudml.org/doc/248664},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Rudolf, Boris
TI - Monotone iterative technique and connectedness of the set of solutions
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 3
SP - 323
EP - 329
AB - The paper deals with the properties of a monotone operator defined on a subset of an ordered Banach space. The structure of the set of fixed points between the minimal and maximal ones is described.
LA - eng
KW - order preserving operator; ordered Banach space; structure of the set of fixed points; fixed points between the minimal and maximal ones; connectedness of the set of solutions; order preserving operator; ordered Banach space; structure of the set of fixed points; fixed points between the minimal and maximal ones; connectedness of the set of solutions
UR - http://eudml.org/doc/248664
ER -

References

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  7. Ladde G. S., Lakshmikantham V., Vatsala A. S., Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston, 1986. (1986) MR0855240
  8. Lakshmikantham V., Leela S., 10.1016/0362-546X(84)90050-6, Nonlinear Anal. 8 (1984), 281-287. (1984) Zbl0532.34029MR0738013DOI10.1016/0362-546X(84)90050-6
  9. Rudolf B., Kubáček Z., 10.1016/0022-247X(90)90341-C, J. Math. Anal. Appl. 146 (1990), 203-206. (1990) Zbl0713.34015MR1041210DOI10.1016/0022-247X(90)90341-C
  10. Šeda V., 10.1016/S0362-546X(97)00033-3, Nonlinear Anal. 30 (1997), 1607-1616. (1997) MR1490083DOI10.1016/S0362-546X(97)00033-3

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