Classes of sequences of real numbers, games and selection properties

This is a continuation of our investigation of classes of sequences of positive real numbers satisfying some selection principles as well as having certain game-theoretic properties. We improve main results from [D. Djurčić, Lj.D.R. Kočinac, M.R. Žižović, Some properties of rapidly varying sequences, J. Math. Anal. Appl. 327 (2007) 1297–1306] and [D. Djurčić, Lj.D.R. Kočinac, M.R. Žižović, Rapidly varying sequences and rapid convergence, Topology Appl. (2008), doi: 10.1016/j.topol.2007.05.026, in press].