This paper introduces the sequence Banach space $ \ell_{\psi}(\mathbb{Z}) $ for a class of convex functions $ \psi $, and studies the properties of the 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 paper focuses on the structure and behavior of these interpolation spaces, which are essential in the theory of interpolation of operators. The study of these spaces is motivated by the need to understand the relationship between different Banach spaces and the role of convex functions in their construction. The paper also references several key works in the field, including those by Bergh and Löfström, Bonsall and Duncan, Brudnyi and Krugljak, Kato, Saito, and Tamura, among others. These references highlight the broader context of interpolation theory and its applications in functional analysis. The paper contributes to the understanding of $ \psi $-interpolation spaces, which are a generalization of classical interpolation spaces. The study of these spaces is important for the development of interpolation theory and its applications in various areas of mathematics, including harmonic analysis, partial differential equations, and approximation theory. The paper also discusses the significance of convex functions in the construction of these spaces and their role in the interpolation process. The results presented in this paper provide a deeper understanding of the properties of interpolation spaces and their applications in functional analysis.This paper introduces the sequence Banach space $ \ell_{\psi}(\mathbb{Z}) $ for a class of convex functions $ \psi $, and studies the properties of the 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 paper focuses on the structure and behavior of these interpolation spaces, which are essential in the theory of interpolation of operators. The study of these spaces is motivated by the need to understand the relationship between different Banach spaces and the role of convex functions in their construction. The paper also references several key works in the field, including those by Bergh and Löfström, Bonsall and Duncan, Brudnyi and Krugljak, Kato, Saito, and Tamura, among others. These references highlight the broader context of interpolation theory and its applications in functional analysis. The paper contributes to the understanding of $ \psi $-interpolation spaces, which are a generalization of classical interpolation spaces. The study of these spaces is important for the development of interpolation theory and its applications in various areas of mathematics, including harmonic analysis, partial differential equations, and approximation theory. The paper also discusses the significance of convex functions in the construction of these spaces and their role in the interpolation process. The results presented in this paper provide a deeper understanding of the properties of interpolation spaces and their applications in functional analysis.