I-WEIGHTED LACUNARY STATISTICAL tau-CONVERGENCE IN LOCALLY SOLID RIESZ SPACES

Authors : Şükran Konca, Ergin Genç

Pages : 22-31

Doi:10.33773/jum.492457

View : 26 | Download : 11

Publication Date : 2019-01-30

Article Type : Research

Abstract :An ideal $I$ is a family of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this  paper, we introduce the notions of ideal versions of weighted lacunary statistical $\tau$-convergence, statistical $\tau$-Cauchy, weighted lacunary $\tau$-boundedness of sequences in locally solid Riesz spaces endowed with the topology $\tau$. We also prove some topological results related to these concepts in locally solid Riesz space.
Keywords : Ordered topological vector space, locally solid Riesz space, $I$-weighted lacunary statistical $ au$-convergence, I-convergence