(Σ, F)-Asymptotically Lacunary Equivalent Sequences

Abstract

We introduce the strong (sigma,f)- asymptotically equivalent and strong (sigma,f)- asymptotically lacunary equivalent sequences which are some combinations of the definitions for asymptotically equivalent, statistical limit, modulus function sigma-convergence, and lacunary sequences. Thenwe use these definitions to prove strong (sigma,f)- asymptotically equivalent and strong (sigma,f)- asymptotically lacunary equivalent analogues of Connor's results in Connor, 1988, Fridy and Orhan's results in Fridy and Orhan, 1993, and Das and Patel's results in Das and Patel, 1989.