This paper introduces the sequence Banach space $\ell_{\psi}(\mathbb{Z})$ for a class of convex functions $\psi$. It investigates the properties of K- and J-interpolation spaces $(E_0, E_1)_{\theta, \psi, K}$ and $(E_0, E_1)_{\theta, \psi, J}$ for a Banach couple $\overline{E} = (E_0, E_1)$ and $\theta \in (0, 1)$. The study is classified under the mathematics subject code 46B70 and includes keywords such as interpolation spaces, Banach spaces, Banach couple, and convex functions. The references cited include works by V. Ovchinnikov, K.-S. Saito, M. Kato, Y. Takahashi, H. Triebel, and T. Zachariades.This paper introduces the sequence Banach space $\ell_{\psi}(\mathbb{Z})$ for a class of convex functions $\psi$. It investigates the properties of K- and J-interpolation spaces $(E_0, E_1)_{\theta, \psi, K}$ and $(E_0, E_1)_{\theta, \psi, J}$ for a Banach couple $\overline{E} = (E_0, E_1)$ and $\theta \in (0, 1)$. The study is classified under the mathematics subject code 46B70 and includes keywords such as interpolation spaces, Banach spaces, Banach couple, and convex functions. The references cited include works by V. Ovchinnikov, K.-S. Saito, M. Kato, Y. Takahashi, H. Triebel, and T. Zachariades.