New Definitions about AI-Statistical Convergence with Respect to a Sequence of Modulus Functions and Lacunary Sequences

In this paper, using an infinite matrix of complex numbers, a modulus function and a lacunary sequence, we generalize the concept of I-statistical convergence, which is a recently introduced summability method. The names of our new methods are A(I)-lacunary statistical convergence and strongly A(I)-lacunary convergence with respect to a sequence of modulus functions. These spaces are denoted by S-theta(A)(I, F) and N-theta(A)(I, F), respectively. We give some inclusion relations between S-theta(A) (I, F), S-theta(A) (I, F) and N-theta(A) (I, F). We also investigate Cesaro summability for A(I) and we obtain some basic results between A(I)-Cesaro summability, strongly A(I)-Cesaro summability and the spaces mentioned above.