Abstract:
This paper presents new definitions which are a natural combination of the definition for asymptoticall equivalence and Delta-statistical convergence of sequences. Let theta = (k(r)) be a lacunary sequence. Then the sequences x and y are said to be [w](0,Delta)(L) -asymptotically equivalent of multiple L provided that for every epsilon > 0
lim(r) 1/h(r)|{k is an element of I(r) : |t(km) (Delta(xk))/t(km) (Delta(yk)) - L| >= epsilon}| = 0.
