Furi–Pera fixed point theorems in Banach algebras with applications

Smaïl Djebali; Karima Hammache

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2008)

  • Volume: 47, Issue: 1, page 55-75
  • ISSN: 0231-9721

Abstract

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In this work, we establish new Furi–Pera type fixed point theorems for the sum and the product of abstract nonlinear operators in Banach algebras; one of the operators is completely continuous and the other one is 𝒟 -Lipchitzian. The Kuratowski measure of noncompactness is used together with recent fixed point principles. Applications to solving nonlinear functional integral equations are given. Our results complement and improve recent ones in [10], [11], [17].

How to cite

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Djebali, Smaïl, and Hammache, Karima. "Furi–Pera fixed point theorems in Banach algebras with applications." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 47.1 (2008): 55-75. <http://eudml.org/doc/32472>.

@article{Djebali2008,
abstract = {In this work, we establish new Furi–Pera type fixed point theorems for the sum and the product of abstract nonlinear operators in Banach algebras; one of the operators is completely continuous and the other one is $\{\mathcal \{D\}\}$-Lipchitzian. The Kuratowski measure of noncompactness is used together with recent fixed point principles. Applications to solving nonlinear functional integral equations are given. Our results complement and improve recent ones in [10], [11], [17].},
author = {Djebali, Smaïl, Hammache, Karima},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {banach algebra; Furi–Pera condition; fixed point theorem; measure of noncompactness; integral equations; Banach algebra; fixed point; Furi-Pera condition},
language = {eng},
number = {1},
pages = {55-75},
publisher = {Palacký University Olomouc},
title = {Furi–Pera fixed point theorems in Banach algebras with applications},
url = {http://eudml.org/doc/32472},
volume = {47},
year = {2008},
}

TY - JOUR
AU - Djebali, Smaïl
AU - Hammache, Karima
TI - Furi–Pera fixed point theorems in Banach algebras with applications
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2008
PB - Palacký University Olomouc
VL - 47
IS - 1
SP - 55
EP - 75
AB - In this work, we establish new Furi–Pera type fixed point theorems for the sum and the product of abstract nonlinear operators in Banach algebras; one of the operators is completely continuous and the other one is ${\mathcal {D}}$-Lipchitzian. The Kuratowski measure of noncompactness is used together with recent fixed point principles. Applications to solving nonlinear functional integral equations are given. Our results complement and improve recent ones in [10], [11], [17].
LA - eng
KW - banach algebra; Furi–Pera condition; fixed point theorem; measure of noncompactness; integral equations; Banach algebra; fixed point; Furi-Pera condition
UR - http://eudml.org/doc/32472
ER -

References

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