The integer sequence is called a lacunary sequence if it is increasing and . A complex number sequence is said to be -convergent to if for each one has
Let be the family of all sequences which are -convergent to some . In this paper, which continues the work of J. A. Fridy and C. Orhan [Pac. J. Math. 160, No. 1, 43-51 (1993; Zbl 0794.60012)], the author studies inclusion properties between and , where and are two arbitrary lacunary sequences.