On asymptotically generalized statistical equivalent sequences via ideals

For an admissible ideal ${mathcal I}subseteq {mathcal P}({mathbb N})$ and a non-decreasing realsequence $lambda =(lambda_n)$ tending to $infty$ with $lambda_{n+1} leq lambda_n+1, lambda_1 = 1$, the objective of this paper is to introduce the new notions ${mathcal I}-$statistically equivalent, ${mathcal I}-[V, lambda]-$equivalent and ${mathcal I}-lambda -$statistically equivalent. which are natural combinations of the definitions for asymptotically equivalent, statistical limit, $lambda-$statistical limit and ${mathcal I}-$limit for number sequences. In addition, some relations among these new notions are also obtained.