Lacunary statistical boundedness on time scales

In this paper, we introduce the concept of lacunary statistical boundedness of Δ-measurable real-valued functions on an arbitrary time scale. We also give the relations between statistical boundedness and lacunary statistical boundedness on time scales.

Density by Moduli and Statistical Boundedness

We have generalized the notion of statistical boundedness by introducing the concept off-statistical boundedness for scalar sequences wherefis an unbounded modulus. It is shown that bounded sequences are precisely those sequences which aref-statistically bounded for every unbounded modulusf. A decomposition theorem forf-statistical convergence for vector valued sequences and a structure theorem forf-statistical boundedness have also been established.

Weighted lacunary statistical convergence of double sequences in locally solid Riesz spaces

Recently, the notion of weighted lacunary statistical convergence is studied in a locally solid Riesz space for single sequences by Ba?ar?r and Konca [7]. In this work, we define and study weighted lacunary statistical ?-convergence, weighted lacunary statistical ?-boundedness of double sequences in locally solid Riesz spaces. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces and give some inclusion relations.