On Lacunary Statistical Convergence in Metric-Like Spaces

Abstract

In the present study, we generalize the notions of lacunary statistical $\sigma$-convergence and lacunary statistical $\sigma$-boundedness of real valued sequences to that of vector valued sequences in an arbitrary metric-like space $(X,\sigma)$. We also explore that a bounded and lacunary statistically $\sigma$-convergent sequence is lacunary strongly $\sigma$-Cesàro summable in a metric-like space. Beside this some inclusion relations are also established between the notion of lacunary statistical $\sigma$-convergence and lacunary strongly $\sigma$-Cesàro summability in $(X,\sigma)$.