Ideal convergence of quantum difference sequences of bi-complex numbers
Abstract
We investigate different properties of ideal convergent second-order quantum difference se- q uence spaces over bi-complex numbers. We define Z[\nabla_q^2, \|\cdot\|_{C_2}] for Z \in \{I_c^*, I_\theta^*, I_1^*, I_p^*, I_\infty^*\} , using the second-order q -difference operator \nabla_q^2 under the Euclidean norm. We examine their BK-space structure, symmetric property, inclusion relations, and isomorphisms with classical I-convergent bi-complex sequence spaces. A matrix representation of the operator is given, along with counterexamples, to demonstrate contradictions in specific inclusion cases.
Fields of Study & Subjects
Approximation Theory and Sequence Spaces
Holomorphic and Operator Theory
Advanced Banach Space Theory
Publication details
- Journal / source
- Filomat
- Publisher
- National Library of Serbia
- Volume
- 40
- Issue
- 1
- Pages
- 355–370
- Publication date
- 1 January 2026
- Language
- EN