On lacunary statistical convergence and lacunary stron Cesàro convergence by moduli

Here we fully complete the studies initiated by Vinod K. Bhardwaj and Shweta Dhawan in \cite{hindawi} which relate different convergence methods which involves the classical statistical and the classical strong Cesàro convergences by means of lacunary sequences and measures of density in $\mathbb{N}$ modulated by a modulus function $f$.