Fatih Nuray, Department of Mathematics, Afyon Kocatepe University, Afyonkarahisar, Turkey, e-mail: fnuray@aku.edu.tr
Abstract: The aim of this work is to generalize lacunary statistical convergence to weak lacunary statistical convergence and $\mathcal I$-convergence to weak $\mathcal I$-convergence. We start by defining weak lacunary statistically convergent and weak lacunary Cauchy sequence. We find a connection between weak lacunary statistical convergence and weak statistical convergence.
Keywords: weak convergence, statistical convergence, lacunary sequence, lacunary statistical convergence
Classification (MSC 2010): 40A05, 46A25
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