Fixed Point Theorems of the Banach and Krasnosel’skii Type for Mappings on m -tuple Cartesian Product of Banach Algebras and Systems of Generalized Gripenberg’s Equations

Eva Brestovanská; Milan Medveď

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2012)

  • Volume: 51, Issue: 2, page 27-39
  • ISSN: 0231-9721

Abstract

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In this paper we prove some fixed point theorems of the Banach and Krasnosel’skii type for mappings on the m -tuple Cartesian product of a Banach algebra X over ℝ . Using these theorems existence results for a system of integral equations of the Gripenberg’s type are proved. A sufficient condition for the nonexistence of blowing-up solutions of this system of integral equations is also proved.

How to cite

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Brestovanská, Eva, and Medveď, Milan. "Fixed Point Theorems of the Banach and Krasnosel’skii Type for Mappings on $m$-tuple Cartesian Product of Banach Algebras and Systems of Generalized Gripenberg’s Equations." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 51.2 (2012): 27-39. <http://eudml.org/doc/246177>.

@article{Brestovanská2012,
abstract = {In this paper we prove some fixed point theorems of the Banach and Krasnosel’skii type for mappings on the $m$-tuple Cartesian product of a Banach algebra $X$ over $\mathbb \{R\}$. Using these theorems existence results for a system of integral equations of the Gripenberg’s type are proved. A sufficient condition for the nonexistence of blowing-up solutions of this system of integral equations is also proved.},
author = {Brestovanská, Eva, Medveď, Milan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {fixed point; Banach algebra; integral equation; integro-differential system; epidemic model; blowing-up solution; fixed point; Banach algebra; integral equation; integro-differential system; epidemic model; blowing-up solution},
language = {eng},
number = {2},
pages = {27-39},
publisher = {Palacký University Olomouc},
title = {Fixed Point Theorems of the Banach and Krasnosel’skii Type for Mappings on $m$-tuple Cartesian Product of Banach Algebras and Systems of Generalized Gripenberg’s Equations},
url = {http://eudml.org/doc/246177},
volume = {51},
year = {2012},
}

TY - JOUR
AU - Brestovanská, Eva
AU - Medveď, Milan
TI - Fixed Point Theorems of the Banach and Krasnosel’skii Type for Mappings on $m$-tuple Cartesian Product of Banach Algebras and Systems of Generalized Gripenberg’s Equations
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2012
PB - Palacký University Olomouc
VL - 51
IS - 2
SP - 27
EP - 39
AB - In this paper we prove some fixed point theorems of the Banach and Krasnosel’skii type for mappings on the $m$-tuple Cartesian product of a Banach algebra $X$ over $\mathbb {R}$. Using these theorems existence results for a system of integral equations of the Gripenberg’s type are proved. A sufficient condition for the nonexistence of blowing-up solutions of this system of integral equations is also proved.
LA - eng
KW - fixed point; Banach algebra; integral equation; integro-differential system; epidemic model; blowing-up solution; fixed point; Banach algebra; integral equation; integro-differential system; epidemic model; blowing-up solution
UR - http://eudml.org/doc/246177
ER -

References

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  8. Krasnosel’skii, M. A., Two remarks on the method of succesive approximations, Uspechi Mat. Nauk 10 (1955), 123–127. (1955) MR0068119
  9. Olaru, I. M., An integral equation via weakly Picard operators, Fixed Point Theory 11, 1 (2010), 97–106. (2010) Zbl1196.45009MR2656009
  10. Olaru, I. M., Generalization of an integral equation related to some epidemic models, Carpatian J. Math. 26 (2010), 0–4. (2010) Zbl1224.34205MR2676722
  11. Zeidler, E., 10.1007/978-1-4612-0815-0, Applied Mathematical Sciences, Vol. 108, Springer-Verlag, New York, 1995. (1995) Zbl0834.46002MR1347691DOI10.1007/978-1-4612-0815-0

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