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 : 14 | Download : 4

Publication Date : 2019-01-30

Article Type : Research Paper

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