P-asymptotically Equivalent in Probability - Patterson, Richard F.; Savaş, Ekrem (Sarajevo Journal of Mathematics, 2024)
In this paper we present the following definitions P-asymptotically equivalent probability of multiple L and P-asymptotically probability regular. In addition to these definitions we asked and provide answers for the following questions. (1)If xProbability≈ y then what type of four dimensional matrices transformation will satisfy the following μ (Ax)Probability≈ μ (Ay)? (2) If [x] and [y] are bounded double sequences that P-asymptotically converges at the same rate, then what are the necessary and sufficient conditions on the entries of any four dimensional matrix transformation A that will ensure that A sums [x] and [y] at the same P-asymptotic rate? (3) What are the conditions on the entries of four dimensional matrices that ensure the preservation of P-asymptotically convergence in probability?