On $\mathcal{I^K}$-supremum, $\mathcal{I^K}$-infimum and related results

In this paper, we introduce the concept of $\mathcal{I^K}$-supremum, $\mathcal{I^K}$-infimum, $\mathcal{I^K}-$limit superior, and $\mathcal{I^K}-$limit inferior and investigate a few implication relationships between them.