Research Article

Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations

Volume: 32 Number: 4 December 1, 2019
EN

Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations

Abstract

This paper examines Hyers-Ulam (HU), Hyers-Ulam-Rassias (HUR) and Hyers-Ulam-Rassias-Gavruta (HURG) stability of the first-order differential equation including Bernoulli’s, Riccati and Abel with given initial condition.

Keywords

References

  1. Referans1 Alqifiary, Q.H.: Note on the stability for linear systems of differential equations. International Journal of Applied Mathematical Research. 3, no. 1, 15-22 (2014).
  2. Referans2 Alsina, C., Ger, R.: On some inequalities and stability results related to the exponential function. J. Inequal. Appl. 2, no.4, 373-380 (1998).
  3. Referans3 András, S., Mészáros, A.R.: Ulam-Hyers stability of dynamic equations on time scales via Picard operators. Appl. Math. Comput. 219, 4853-4864 (2013).
  4. Referans4 Aoki, T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan. 2, 64-66 (1950).
  5. Referans5 Bourgin, D.G.:Classes of transformations and bordering transformations. Bull. Amer. Math. Soc. 57, 223-237 (1951).
  6. Referans6 Cãdariu, L., Radu, V.: On the Stability of the Cauchy Functional Equation: A Fixed Point Approach, Iteration theory (ECIT ’02), Grazer Math. Ber. 346, 43-52 (2004).
  7. Referans7 Hyers, D.H.: On the stability of the linear functional equation. Proc. Nat. Acad. Sci. U.S.A. 27, 222-224 (1941).
  8. Referans8 Jung, S.M.: Hyers-Ulam stability of linear differential equations of first order. Appl. Math. Lett. 17, no. 10, 1135-1140 (2004).

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Publication Date

December 1, 2019

Submission Date

December 7, 2018

Acceptance Date

April 11, 2019

Published in Issue

Year 2019 Volume: 32 Number: 4

APA
Bascı, Y., Ögrekcı, S., & Mısır, A. (2019). Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science, 32(4), 1238-1252. https://doi.org/10.35378/gujs.493396
AMA
1.Bascı Y, Ögrekcı S, Mısır A. Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science. 2019;32(4):1238-1252. doi:10.35378/gujs.493396
Chicago
Bascı, Yasemin, Suleyman Ögrekcı, and Adil Mısır. 2019. “Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations”. Gazi University Journal of Science 32 (4): 1238-52. https://doi.org/10.35378/gujs.493396.
EndNote
Bascı Y, Ögrekcı S, Mısır A (December 1, 2019) Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science 32 4 1238–1252.
IEEE
[1]Y. Bascı, S. Ögrekcı, and A. Mısır, “Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations”, Gazi University Journal of Science, vol. 32, no. 4, pp. 1238–1252, Dec. 2019, doi: 10.35378/gujs.493396.
ISNAD
Bascı, Yasemin - Ögrekcı, Suleyman - Mısır, Adil. “Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations”. Gazi University Journal of Science 32/4 (December 1, 2019): 1238-1252. https://doi.org/10.35378/gujs.493396.
JAMA
1.Bascı Y, Ögrekcı S, Mısır A. Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science. 2019;32:1238–1252.
MLA
Bascı, Yasemin, et al. “Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations”. Gazi University Journal of Science, vol. 32, no. 4, Dec. 2019, pp. 1238-52, doi:10.35378/gujs.493396.
Vancouver
1.Yasemin Bascı, Suleyman Ögrekcı, Adil Mısır. Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science. 2019 Dec. 1;32(4):1238-52. doi:10.35378/gujs.493396

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