On the solution of linear functional two-term equations with shift

Oleksandr Karelin; Anna Tarasenko

doi:10.29057/icbi.v11iEspecial3.11495

Oleksandr Karelin Universidad Autónoma del Estado de Hidalgo https://orcid.org/0000-0001-5055-8123
Anna Tarasenko Universidad Autónoma del Estado de Hidalgo https://orcid.org/0000-0002-7300-9298

DOI: https://doi.org/10.29057/icbi.v11iEspecial3.11495

Keywords: Linear functional operator with shift, Non-Carlemann shift, Hölder space, Infinite product, Systems with renewable resources

Abstract

This work is dedicated to the study of linear functional equations with shift in Hölder space. Previously, for such operators, conditions for invertibility were found and the inverse operator was constructed by the authors. The operators are used in modeling systems with renewable resources. Here we propose another approach to solving functional equations with shift. With the help of an algorithm, the initial equation is reduced to the first iterated equations, then to the second iterated equation. Continuing this process, we obtain the n-th iterated equation and the limit iterated equation. We prove the theorem on the equivalence of the original and the iterated equations. Based on the analysis of the solvability of the limit equation, we find a solution to the original equation. The solution is the sum of an infinite product and a functional series. The results, and the methods for obtaining them, are transparent and not as cumbersome compared to previous works.

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References

Tarasenko, A., Karelin, O., Pérez-Lechuga, P., y González-Hernández, M. (2010). Modelling systems with renewable resources based on functional operators with shift. Applied Mathematics and Computation, 216(7), 1938-1944. DOI: 10.1016/j.amc.2010.03.023

Karelin, O., González-Hernández, M., Hernández-Romero, N., y Seck Tuoh-Mora, J. (2015). Study of renewable systems based on functional operators with shift. Applied Mathematical Sciences, 9(144), 7167-7173. DOI: 10.12988/ams.2015.510622

Karelin, O., Tarasenko, A., Barabash, O., González-Hernández, M., y Medina-Marin, J. (2019). Study of Changes of Individual Parameter of Resources in the Modelling of Renewable Systems. En Ao, S., Gelman, L., y Kim, H. (Eds.), Transactions on Engineering Technologies (pp. 19-28). Springer Nature Singapore.

Karelin, O., Tarasenko, A., Zolotov, V., y González-Hernández, M. (2018). Study of the equilibrium state of systems with two renewable resources based on functional operators with shift. IAENG International Journal of Applied Mathematics, 48(1), 98-104.

Karelin, O., Tarasenko, A., Zolotov, V., y González-Hernández, M. (2019). Mathematical Models for the Study of Resource Systems Based on Functional Operators with Shift. En Ao, S.-I., et al. (Eds.), Transactions on Engineering Technologies (pp. 95-108). Springer Nature.

Tarasenko, G., y Karelin, O. (2016). Condition of Invertibility for Functional Operators with Shift in Weighted Hölder spaces. Ukrainian Mathematical Journal, 67(11), 1758-1769.

Karelin, O., Tarasenko, A., y González-Hernández, M. (2022). On invertibility of some functional operators with shift. Applied Mathematics, 13(8), 651-657. DOI: 10.4236/am.2022.138040

Tarasenko, A., Karelin, O., González-Hernández, M., y Karelina, D. (2023). On the Solution of Equations with Linear-Fractional Shifts. WSEAS Transaction on Mathematics, 22, 254-258. DOI: 10.37394/23206.2023.22.30

Khinchin, A. Yu. (1964). Continued Fraction. University of Chicago Press.

Tarasenko, A., Karelin, O., González-Hernández, M., y Barabash, O. (2021). Modelling Systems with Elements in Several States. WSEAS Transaction on Environment and Development, 17, 244-252. DOI: 10.37394/232015.2021.17.25