Abstract:
In this paper, we extend statistical bounded sequences of real or complex numbers to the setting of sequences of bi-complex numbers. We define the statistical bounded sequence space of bi-complex numbers b∗∞b∗∞ and also define the statistical bounded sequence spaces of ideals I1∞ and I2∞. We prove some inclusion relations and provide examples. We establish that b∗∞ is the direct sum of I1∞ and I2∞. Also, we prove the decomposition theorem for statistical bounded sequences of bi-complex numbers. Finally, summability properties in the light of J.A. Fridy's work are studied.
J. Hossain, S. Debnath, “On $\mathcal{I}^{\mathcal{K}}$-convergence of sequences of bi-complex numbers”, Probl. anal. Issues Anal., 13(31):3 (2024), 43–55