Generalized difference Cesaro sequence spaces in 2-normed spaces

In this paper, we have introduced new Cesaro-type sequence spaces formed by combining a generalized difference operator $$\Delta ^r$$ with a Cesaro summability operator $$\phi $$ of order $$\alpha >-1$$ in the setting of 2-normed spaces. Using a bounded sequence of positive real numbers $$p=(p_n),$$ we define the spaces $$\ell _\infty (\Delta ^r,\phi ,p,\Vert \cdot ,\cdot \Vert )$$ and $$\ell (\Delta ^r,\phi ,p,\Vert \cdot ,\cdot \Vert ).$$ Some special cases for lower-order difference operators are also discussed to show the general nature of our construction. We study the algebraic and topological properties of these spaces in detail. In particular, we examine basic properties such as linearity, paranormed structure, completeness, Banach-type behavior, and inclusion relations between the newly defined spaces and known sequence spaces. The inclusion results help to explain the relationships among these spaces. Overall, this work extends several existing results in summability theory and supports further studies in sequence spaces defined on 2-normed and paranormed spaces.