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

Abstract

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 AI-lacunary statistical convergence and strongly AI -lacunary convergence with respect to a sequence of modulus functions. These spaces are denoted by SθA (I, F) and NθA (I, F), respectively. We give some inclusion relations between SA (I, F), θA (I, F) and NθA (I, F). We also investigate Cesáro summability for AI and we obtain some basic results between AI -Cesáro summability, strongly AI -Cesáro summability and the spaces mentioned above.