WEIGHTED LACUNARY STATISTICAL CONVERGENCE IN LOCALLY SOLID RIESZ SPACES

Abstract

In this paper, by combining both of the denitions of lacunary
sequence and Norlund-type mean, we obtain a new lacunary sequence and a new concept of statistical convergence which will be called weighted lacunary statistical convergence. In the light of these new concepts, we introduce the concepts of weighted lacunary statistical tau-convergence, weighted lacunary statistical tau-bounded and also weighted statistical tau-convergence, which is a special case of weighted lacunary statistical tau-convergence, in the framework of locally solid Riesz spaces and prove some topological results related to these concepts.