- 22/05/2024, das 14h30 às 15h30 (CLAV -- Anfiteatro 1 e online)
Alberto Simões, Auxiliar Professor, University of Beira Interior, Department of Mathematics and Center of Mathematics and Applications of University of Beira Interior (CMA-UBI), Portugal, This email address is being protected from spambots. You need JavaScript enabled to view it.
Abstract: An interesting and famous talk presented by S. M. Ulam in 1940 triggered the study of stability problems for various functional equations. In the following year, D. H. Hyers was able to give a partial solution to Ulam’s question that was the first significant breakthrough and step toward more solutions in this area. After that preliminary answer, other approaches emerged, and new orientations were introduced by Th. M. Rassias, in- troducing therefore the so-called Hyers-Ulam-Rassias stability. Different generalizations were obtained by other researchers, by considering the possibility of using different involved norms, others types of equations, but always resorting to the useful Banach Fixed Point Theorem. In this talk our main goal is to present the various approaches and techniques used to study Hyers-Ulam, Hyers-Ulam-Rassias and σ-semi-Hyers-Ulam stabilities for different types of equations.
The talk is based on joint works with L. P. Castro from University of Aveiro and Center for Research and Development in Mathematics and Applications, Portugal.
Keywords: Hyers-Ulam stability, σ-semi-Hyers-Ulam stability, Hyers-Ulam-Rassias stabil- ity, Banach fixed point theorem, higher order integro-differential equations, Bessel differen- tial equation, fractional boundary value problem.
References
[1] A. M. Simões (2023). Different stabilities for oscillatory Volterra integral equations. Mathematical Methods in the Applied Sciences, pp. 1-12. DOI: 10.1002/mma.9094
[2] Alberto Simões, Ponmana Selvan (2022). Hyers-Ulam stability of a certain Fredholm integral equation. Turkish Journal of Mathematics, 46, 87-89. DOI: 10.3906/mat-2106- 120
[3] A. M. Simões, Ponmana Selvan, Soon-Mo Jung, Joiok Roh (2022). On the stability of Bessel differential equation. Journal of Applied Analysis & Computation, 12(5), pp. 2014-2023. DOI: 10.11948/20210437
[4] A. M. Simões, F. Carapau, P. Correia (2021). New Sufficient Conditions to Ulam Sta- bilities for a Class of Higher Order Integro-Differential Equations. Symmetry, 13(11), 2068. DOI: https://doi.org/10.3390/sym13112068
[5] L. P. Castro, A. M. Simões (2019). Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential Equations. Kenan Tas (ed.) et al., Methods in Engineering: Theoretical Aspects, 81-94, Nonlinear Syst. Complex., 23, Springer, Cham. ISBN 978- 3-319-91064-2. DOI: 10.1007/978-3-319-91065-9-3.
[6] L. P. Castro, A. M. Simões (2018). Hyers-Ulam-Rassias stability of nonlinear integral equations through the Bielecki metric. Mathematical Methods in the Applied Sciences, 41(17), pp. 7367–7383. DOI: https://doi.org/10.1002/mma.4857
[7] L. P. Castro, A. M. Simões (2017). Different Types of Hyers-Ulam-Rassias Stabilities for a Class of Integro-Differential Equations. Filomat, 31(17), pp. 5379–5390. DOI: 10.2298/FIL1717379C.
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