Mathematics and Computational Sciences

A refined approach to Ulam-Hyers stability in trigonometric AQ functional equations

Articles in Press

Document Type : Original Article

Authors

P Agilan 1
V Vallinayagam 1
S Annadurai 1
Vaddi Seshagiri Rao 2

1 Department of Mathematics, St.Joseph’s College of Engineering, OMR, Chennai, 600 119, Tamilnadu, India.

2 Department of Mechanical Engineering, St.Joseph's College of Engineering, OMR, Chennai-600119

https://doi.org/10.30511/mcs.2026.2079529.1648
Abstract
The primary objective of this paper is to formulate an extended version of a new mixed-type additive-quadratic functional equation and to analyze its Ulam-Hyers stability in three distinct cases: odd, even, and odd-even. Specifically, the odd case corresponds to the stability of additive functional equations, the even case corresponds to the stability of quadratic functional equations, and the odd-even case characterizes the stability behavior of mixed additive-quadratic (AQ) functional equations

Keywords

Additive
Quadratic Functional Equations
Generalized Hyers - Ulam Stability
Subjects
[1] Agarwal, R.P., Hristova, S. and O’Regan, D., (2024). Ulam stability for boundary value problems of differential equationsmain misunderstandings and how to avoid them. Mathematics, 12(11), p.1626.
[2] Agarwal, G., Singh, M.M., Jan, R. and Purohit, S.D., (2025). Nonlinear dynamics and stability analysis of a pandemic model using homotopy perturbation. Critical Reviews in Biomedical Engineering, 53(3). 
[3] Agilan, P., Julietraja, K., Mlaiki, N. and Mukheimer, A., (2022). Intuitionistic fuzzy stability of an Euler–Lagrange symmetry additive functional equation via direct and fixed point technique. Symmetry, 14, p.2454. 
[4] Agilan, P., Julietraja, K., Kanimozhi, B. and Alsinai, A., (2024). Hyers stability of AQC functional equation. Dynamics of Continuous, Discrete and Impulsive Systems, Series B, 31, pp.63–75. 
[5] Agilan, P., Almazah, M.A.A., Julietraja, K. and Alsinai, A., (2023). Classical and fixed point approach to the stability analysis of a bilateral symmetric additive functional equation in fuzzy and random normed spaces. Mathematics, 11, p.681. 
[6] Agilan, P., Julietraja, K., Almazah, M.A.A. and Alsinai, A., (2023). Stability analysis of a new class of series type additive functional equation in Banach spaces: direct and fixed point techniques. Mathematics, 11, p.887. 
[7] Agilan, P., Julietraja, K., Aljohani, S. and Mlaiki, N., (2024). Generalised Ulam-Hyers stability analysis for system of additive functional equation in fuzzy and random normed spaces: direct and fixed point approach. International Journal of Analysis and Applications, 22, p.201. 
[8] Agilan, P., Vijayan, V., Sophia, M. and Ganapathy, G., (2025). Exploring advanced stability of higher-order functional equations in neutrosophic normed spaces via Hyers-Ulam methodologies. Communications on Applied Nonlinear Analysis, 32(7s), pp.806–822. 
[9] Aoki, T., (1950). On the stability of the linear transformation in Banach spaces. Journal of the Mathematical Society of Japan, 2, pp.64–66. 
[10] Baias, A.R. and Popa, D., (2020). On Ulam stability of a linear difference equation in Banach spaces. Bulletin of the Malaysian Mathematical Sciences Society, 43(2), pp.1357–1371. 
[11] Bhatter, S., Bhatia, B., Kumawat, S. and Purohit, S.D., (2025). Modeling and simulation of COVID-19 disease dynamics via Caputo-Fabrizio fractional derivative. Computational Methods for Differential Equations, 13(2). 
[12] G˘ avruta, P., (1999). An answer to a question of J.M. Rassias concerning the stability of Cauchy functional equation. Advances in Equations and Inequalities, pp.67–71. 
[13] G˘ avruta, P., (2001). On a problem of G. Isac and Th.M. Rassias concerning the stability of mappings. Journal of Mathematical Analysis and Applications, 261, pp.543–553. 
[14] Hyers, D.H., (1941). On the stability of the linear functional equation. Proceedings of the National Academy of Sciences of the USA, 27, pp.222–224. 
[15] Kalvandi, V. and Samei, M.E., (2021). Mittag-Leffler-Hyers-Ulam-Rassias stability of cubic functional equation. Mathematics and Computational Sciences, 2(3), pp.14–21. 
[16] Kumam, P., Ali, A., Shah, K. and Khan, R.A., (2017). Existence results and Hyers–Ulam stability to a class of nonlinear arbitrary order differential equations. Journal of Nonlinear Sciences and Applications, 10(6), pp.2986–2997. 
[17] Kumawat, S., Bhatter, S., Bhatia, B., Purohit, S.D., Baskonus, H.M. and Suthar, D.L., (2025). Novel application of q-HAGTM to analyze Hilfer fractional differential equations in diabetic dynamics. Mathematics and Computers in Simulation, 238, pp.136–149.
[18] Movahednia, E., (2024). Introduce gradual Banach lattices and Hyers stability. Mathematics and Computational Sciences, 5(4), pp.85–97. 
[19] Panda, S., Agarwal, P. and Sinha, A.K., (2025). On q-double modified Laplace transform. Mathematics and Computational Sciences, 6(2), pp.92–101. 
[20] Pasupathi, A., Konsalraj, J., Fatima, N., Velusamy, V., Mlaiki, N. and Souayah, N., (2022). Direct and fixed-point stability instability of additive functional equation in Banach and quasi-beta normed spaces. Symmetry, 14, p.1700. 
[21] Rassias, J.M., (1982). On approximately linear mappings by linear mappings. Journal of Functional Analysis, 46, pp.126–130.
[22] Rassias, J.M., 1984. On approximately linear mappings by linear mappings. Bulletin des Sciences Mathématiques, 108, pp.445–446. 
[23] Rus, I.A., (2009). Ulam stability of ordinary differential equation. Studia Universitatis Babe-Bolyai Mathematica.
[24] Tripathy, A.K., (2021). Hyers-Ulam Stability of Ordinary Differential Equations. Boca Raton: Chapman and Hall/CRC. 
[25] Ulam, S.M., (1964). Problems in Modern Mathematics. New York: Wiley.
Mathematics and Computational Sciences

Articles in Press, Accepted Manuscript
Available Online from 29 May 2026

  • Receive Date 01 December 2025
  • Revise Date 29 May 2026
  • Accept Date 29 May 2026

Home

Submit Manuscript

Reviewers

Contact Us