Hahn Sequence Space of Modals

Area of Science:

• Mathematics
• Interval Analysis
• Sequence Spaces

Background:

• Modal intervals are fundamental in interval calculus with historical roots.
• Modal interval analysis is crucial for Computer Graphics and Computer-Aided Design (CAD), particularly for bounding Bezier and B-Spline curves.

Purpose of the Study:

• Introduce a new sequence space, the Hahn sequence space of modal intervals, denoted h(gI).
• Define new theorems and definitions related to this novel space.
• Investigate the topological properties and inclusion relations of h(gI).

Main Methods:

• Development of new definitions and theorems for modal interval analysis.
• Exploration of inclusion relations within the new sequence space.
• Computation and analysis of the dual spaces of h(gI).

Main Results:

• The introduction of the Hahn sequence space of modal intervals, h(gI).
• Establishment of new theoretical results, including definitions and theorems.
• Characterization of the topological properties and dual spaces of h(gI).

Conclusions:

• The study successfully introduces and defines the Hahn sequence space of modal intervals (h(gI)).
• The topological characteristics and dual spaces of h(gI) have been investigated.
• This work contributes to the theoretical framework of interval analysis and sequence spaces.