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 $x\stackrel{Probability}{≈} y$ then what type of four dimensional matrices transformation will satisfy the following $μ (Ax)\stackrel{Probability}{≈} μ (Ay)$? (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?