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On Iλ-Statistical Convergence in Locally Solid Riesz Spaces

Abstract In this paper, we extend some results concerning statistical convergence in locally solid Riesz spaces by introducing a more general idea of convergence, namely Iλ-statistical convergence. We investigate the ideas of Iλ-statistical-τ-convergence, Iλ-statistical-τ-boundedness and Iλ-statistical-τ-Cauchy condition of sequences in a locally solid Riesz space endowed with a topology τ and investigate some of their consequences.