The Space of Interval-Valued Abel-Convergent Sequences and Their Fundamental Properties

This study introduces and investigates the space of interval-valued Abel-convergent sequences, extending the classical notion of Abel convergence to sequences whose terms are closed and bounded intervals rather than real numbers. A suitable metric structure is defined on this space, and it is shown that the space is complete with respect to the introduced metric. Additionally, it is proven that the space of interval-valued Abel-convergent sequences forms a quasilinear subspace. Moreover, several inclusion relations are examined, and a norm is defined under which the space becomes a normed quasilinear space.