Savaş, Ekrem2015-09-102015-09-1020131305-7820https://hdl.handle.net/11467/1151http://dx.doi.org/10.1186/1687-1847-2013-111This paper presents the following definition, which is a natural combination of the definitions for asymptotically equivalent, I-statistically limit and I-lacunary statistical convergence. Let theta be a lacunary sequence; the two nonnegative sequences x = (x(k)) and y = (y(k)) are said to be I-asymptotically lacunary statistical equivalent of multiple L provided that for every epsilon > 0, and delta > 0, {r is an element of N : 1/h(r)vertical bar{k is an element of l(r) : vertical bar x(k)/y(k) - L vertical bar >=epsilon}vertical bar >=delta}is an element of I (denoted by x (S theta L(I))similar to y) and simply I-asymptotically lacunary statistical equivalent if L = 1.eninfo:eu-repo/semantics/openAccessAsymptotical EquivalentIdeal ConvergenceLacunary SequenceStatistical ConvergenceArticle42267272Q2WOS:000319434900001N/A2-s2.0-84887506461