Affiliation:
1. Department of Mathematics , 72896 Tripura University , Suryamaninagar , Agartala 799022 , India
Abstract
Abstract
In this paper we investigate the concept of
ℐ
{\mathcal{I}}
-monotonic convergence of sequences of bi-complex numbers. We also discuss some partial order relations
≼
i
2
{\preccurlyeq_{i_{2}}}
and
≼
i
id
{\preccurlyeq_{i_{\rm id}}}
between two bi-complex numbers and
ℐ
{\mathcal{I}}
-convergence,
ℐ
{\mathcal{I}}
-monotonic sequences with respect to different partial order relations,
ℐ
{\mathcal{I}}
-Cauchy sequences,
ℐ
{\mathcal{I}}
-bounded monotonic sequences of bi-complex numbers. The analysis indicates that
ℐ
{\mathcal{I}}
-monotonicity with respect to
≼
i
2
{\preccurlyeq_{i_{2}}}
is not comparable with
ℐ
{\mathcal{I}}
-monotonicity with respect to
≼
i
id
{\preccurlyeq_{i_{\rm id}}}
.