MATHEMATICA BOHEMICA, Vol. 136, No. 3, pp. 259-268, 2011

Lacunary weak statistical convergence

Fatih Nuray

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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