Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem

Lydia Bouchal a; Karima Mebarki a; Svetlin Georgiev Georgiev b

Archivum Mathematicum (2022)

  • Volume: 058, Issue: 4, page 199-211
  • ISSN: 0044-8753

Abstract

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In this paper, by using recent results on fixed point index, we develop a new fixed point theorem of functional type for the sum of two operators T + S where I - T is Lipschitz invertible and S a k -set contraction. This fixed point theorem is then used to establish a new result on the existence of positive solutions to a non-autonomous second order difference equation.

How to cite

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Bouchal a, Lydia, Mebarki a, Karima, and Georgiev b, Svetlin Georgiev. "Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem." Archivum Mathematicum 058.4 (2022): 199-211. <http://eudml.org/doc/298895>.

@article{Bouchala2022,
abstract = {In this paper, by using recent results on fixed point index, we develop a new fixed point theorem of functional type for the sum of two operators $T+S$ where $I-T$ is Lipschitz invertible and $S$ a $k$-set contraction. This fixed point theorem is then used to establish a new result on the existence of positive solutions to a non-autonomous second order difference equation.},
author = {Bouchal a, Lydia, Mebarki a, Karima, Georgiev b, Svetlin Georgiev},
journal = {Archivum Mathematicum},
keywords = {fixed point; sum of operators; non-autonomous difference equations; positive solution},
language = {eng},
number = {4},
pages = {199-211},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem},
url = {http://eudml.org/doc/298895},
volume = {058},
year = {2022},
}

TY - JOUR
AU - Bouchal a, Lydia
AU - Mebarki a, Karima
AU - Georgiev b, Svetlin Georgiev
TI - Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 4
SP - 199
EP - 211
AB - In this paper, by using recent results on fixed point index, we develop a new fixed point theorem of functional type for the sum of two operators $T+S$ where $I-T$ is Lipschitz invertible and $S$ a $k$-set contraction. This fixed point theorem is then used to establish a new result on the existence of positive solutions to a non-autonomous second order difference equation.
LA - eng
KW - fixed point; sum of operators; non-autonomous difference equations; positive solution
UR - http://eudml.org/doc/298895
ER -

References

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