The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems

Cristinel Mortici

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 689-695
  • ISSN: 0011-4642

Abstract

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Let T be a γ -contraction on a Banach space Y and let S be an almost γ -contraction, i.e. sum of an ε , γ -contraction with a continuous, bounded function which is less than ε in norm. According to the contraction principle, there is a unique element u in Y for which u = T u . If moreover there exists v in Y with v = S v , then we will give estimates for ∥ u - v ∥ . Finally, we establish some inequalities related to the Cauchy problem.

How to cite

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Mortici, Cristinel. "The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems." Czechoslovak Mathematical Journal 56.2 (2006): 689-695. <http://eudml.org/doc/31059>.

@article{Mortici2006,
abstract = {Let $T$ be a $\gamma $-contraction on a Banach space $Y$ and let $S$ be an almost $\gamma $-contraction, i.e. sum of an $\left( \varepsilon ,\gamma \right) $-contraction with a continuous, bounded function which is less than $\varepsilon $ in norm. According to the contraction principle, there is a unique element $u$ in $Y$ for which $u=Tu.$ If moreover there exists $v$ in $Y$ with $v=Sv$, then we will give estimates for $\Vert u-v\Vert .$ Finally, we establish some inequalities related to the Cauchy problem.},
author = {Mortici, Cristinel},
journal = {Czechoslovak Mathematical Journal},
keywords = {contraction principle; Cauchy problem; contraction principle; Cauchy problem},
language = {eng},
number = {2},
pages = {689-695},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems},
url = {http://eudml.org/doc/31059},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Mortici, Cristinel
TI - The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 689
EP - 695
AB - Let $T$ be a $\gamma $-contraction on a Banach space $Y$ and let $S$ be an almost $\gamma $-contraction, i.e. sum of an $\left( \varepsilon ,\gamma \right) $-contraction with a continuous, bounded function which is less than $\varepsilon $ in norm. According to the contraction principle, there is a unique element $u$ in $Y$ for which $u=Tu.$ If moreover there exists $v$ in $Y$ with $v=Sv$, then we will give estimates for $\Vert u-v\Vert .$ Finally, we establish some inequalities related to the Cauchy problem.
LA - eng
KW - contraction principle; Cauchy problem; contraction principle; Cauchy problem
UR - http://eudml.org/doc/31059
ER -

References

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  1. 10.1007/s10587-005-0058-1, Czechoslovak Math. J. 55 (2005), 709–718. (2005) MR2153095DOI10.1007/s10587-005-0058-1
  2. A coincidence degree for bifurcation problems, Nonlinear Analysis, TMA 53 (2003), 715–721. (2003) MR1959568
  3. Operators of monotone type and periodic solutions for some semilinear problems, Mathematical Reports 54 (1/2002), 109–121. (1/2002) MR1994122
  4. Semilinear equations in Hilbert spaces with quasi-positive nonlinearity, Studia Cluj. 4 (2001), 89–94. (2001) Zbl1027.47044MR1989718
  5. Nonlinear Mappings of Monotone Type, Alphen aan den Rijn, Sijthoff & Noordhoff International Publishers, The Netherlands, 1978. (1978) MR0531036
  6. Ecuaţii Diferenţiale, Integrale şi Sisteme Dinamice. Editura Ex Ponto, Constanţa, Romania, 1999. (1999) MR1734289

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