On \(\mu \)-strong Cesaro summability at infinity and its application to the Fourier–Stieltjes transforms

Abstract

The concept of \(\mu \)-strong Cesaro summability at infinity for a locally integrable function is introduced in this work. The concept of \(\mu \)-statistical convergence at infinity is also considered and the relationship between these two concepts is established. The concept of \(\mu \left[ p\right] \)-strong convergence at infinity point, generated by the measure \(\mu \left( \cdot \right) \) is also considered. Similar results are obtained in this case too. This approach is applied to the study of the convergence of the Fourier–Stieltjes transforms.