ON SOLUTIONS OF INFINITE SYSTEMS OF INTEGRAL EQUATIONS COORDINATEWISE CONVERGING AT INFINITY

Józef Banaś; Agnieszka Chlebowicz; Mohamed-Aziz Taoudi

doi:10.11948/20210385

2022 Volume 12 Issue 5

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Józef Banaś, Agnieszka Chlebowicz, Mohamed-Aziz Taoudi. ON SOLUTIONS OF INFINITE SYSTEMS OF INTEGRAL EQUATIONS COORDINATEWISE CONVERGING AT INFINITY[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 1901-1921. doi: 10.11948/20210385

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Józef Banaś, Agnieszka Chlebowicz, Mohamed-Aziz Taoudi. ON SOLUTIONS OF INFINITE SYSTEMS OF INTEGRAL EQUATIONS COORDINATEWISE CONVERGING AT INFINITY[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 1901-1921. doi: 10.11948/20210385

ON SOLUTIONS OF INFINITE SYSTEMS OF INTEGRAL EQUATIONS COORDINATEWISE CONVERGING AT INFINITY

1.
Department of Nonlinear Analysis, Rzeszów University of Technology, al. Powstańców Warszawy 8, Rzeszów, 35-959, Poland
2.
National School of Applied Sciences, Cadi Ayyad University, Marrakesh, Morocco

Corresponding author: Email: agnchleb@prz.edu.pl (A. Chlebowicz)

Abstract

Abstract

In the paper we are going to prove the existence of solutions of an infinite system of nonlinear quadratic integral equations of Volterra-Hammerstein type. Those solutions are continuous and bounded functions defined on the real half-axis $ \mathbb{R}_+ $ and created by function sequences which are coordinatewise converging to proper limits at infinity. Considerations of the paper are located in the Banach space consisting of functions defined, continuous and bounded on $ \mathbb{R}_+ $ with values in the space of real bounded sequences. The main tool applied in the paper is the technique of measures of noncompactness.
- Function sequence /
- Banach space /
- infinite system of integral equations /
- measure of noncompactness /
- fixed point theorem
MSC: 45G15, 47H08

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References

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