New Definitions aboutAI-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 ofI-statistical convergence, which is a recently introduced summability method. The names of our new methods areAI-lacunary statistical convergence and stronglyAI-lacunary convergence with respect to a sequence of modulus functions. These spaces are denoted bySθAI,FandNθAI,F,respectively. We give some inclusion relations betweenSAI,F,SθAI,FandNθAI,F. We also investigate Cesáro summability forAIand we obtain some basic results betweenAI-Cesáro summability, stronglyAI-Cesáro summability and the spaces mentioned above.