I-Convergence of fractional difference sequences of bi-complex numbers

Tapasi Deb, Binod Chandra Tripathy

Abstract


This study uses the fractional difference operator ∆α for α / ∈ {0,−1,−2,...} to establish new classes of fractional difference sequences Z[BC,I,∆α,∥·∥BC] for Z ∈ {c0,c,ℓ∞}. Solidity and other properties are examined. The spaces have Schauder bases and are BC submodules. To investigate their topological properties and other characteristics, we employ the generalized fractional difference operators ∆ ˜ ˜ (α) and ∆(−˜ α), for a positive proper fraction α. Metrix transformations between the spaces Z[BC,I,∆(˜ α),∥ · ∥BC], for Z ∈ {c0,c,ℓ∞} and the basic sequence spaces Z[BC,I] for Z ∈ {c0,c,ℓ∞} are also explained.

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References


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DOI: https://doi.org/10.52846/ami.v53i1.2108