P. Karthick - Department of Mathematics, Government Arts College for Men, Krishnagiri, India. G. Balasubramanian - Department of Mathematics, Government Arts College for Men, Krishnagiri, India. V. Govindan - Department of Mathematics, , Hindustan Institute of Technology and Science, Padur, Chennai, 603103, Tamil Nadu, India. M. I. Khan - Department of Mechanical Engineering, College of Engineering, Prince Mohammed bin Fahd University, Kingdom of Saudi Arabia. J. L. Amalraj - Department of Science and Humanities, RMK College of Engineering and Technology, Puduvoyal, Thiruvallur, Tamil Nadu, India. A. J. Bala - Department of Mathematics, R.M.D. Engineering College, Kavaraipettai-601206, India.
In this paper, we introduce the new kind of a-type additive functional equation and investigate the Hyers-Ulam stability of a-type additive functional equations within the Banach spaces using the direct method. This approach provides a straightforward and efficient way to establish the stability of functional equations without relying on more complex or indirect techniques. We begin by defining the specific a-type additive functional equation under consideration and outlining the conditions required for its stability. Through rigorous mathematical analysis, we demonstrate that under certain constraints, the functional equation exhibits Hyers-Ulam stability.
P. Karthick, G. Balasubramanian, V. Govindan, M. I. Khan, J. L. Amalraj, A. J. Bala, Hyers-Ulam stability of a-type additive functional equations in Banach space using direct method, Journal of Mathematics and Computer Science, 36 (2025), no. 2, 229--236
Karthick P. , Balasubramanian G., Govindan V., Khan M. I., Amalraj J. L., Bala A. J., Hyers-Ulam stability of a-type additive functional equations in Banach space using direct method. J Math Comput SCI-JM. (2025); 36(2):229--236
Karthick, P. , Balasubramanian, G., Govindan, V., Khan, M. I., Amalraj, J. L., Bala, A. J.. "Hyers-Ulam stability of a-type additive functional equations in Banach space using direct method." Journal of Mathematics and Computer Science, 36, no. 2 (2025): 229--236
