Filomat 2022 Volume 36, Issue 10, Pages: 3217-3230
https://doi.org/10.2298/FIL2210217R
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Meir-Keeler condensing operator to prove existence of solution for infinite systems of differential equations in the Banach space and numerical method to find the solution
Rabbani Mohsen (Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran), Mo.Rabbani@iau.ac.ir
Das Anupam (Department of Mathematics, Cotton University, Guwahati, Assam, India), anupam.das@rgu.ac.in
Hazarika Bipan (Department of Mathematics, Gauhati University, Guwahati, Assam, India), bh_rgu@yahoo.co.in
Arab Reza (Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran), mathreza.arab@gmail.com
In this paper, we establish the existence of solution for infinite systems of
differential equations in the Banach sequence space n(Φ), ℓp(1 ≤ p < ∞)
and c by using Meier-Keeler condensing operators. With the help of examples
we illustrate our results in the sequence spaces. Also for validity of the
results, we find an approximation of solution by using a suitable method
with high accuracy.
Keywords: Measure of noncompactness, Hausdorff measure of noncompactness, Condensing operators, Green’s function, Fixed point
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