New definitions about ai statistical convergence with respect to a sequence of modulus functions and lacunary sequences

In this study, we introduce the notion of A^{I}-lacunary statistical convergence, strongly A^{I}-lacunary convergence with respect to a sequence of modulus functions. We study some collections between them. Also, we give some inclusion relations between A^{I}-lacunary statistical convergence, A^{I}- statistical convergence with respect to a sequence of modulus functions.