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

Abstract

The concept of $$\mu $$ μ -strong Cesaro summability at infinity for a locally integrable function is introduced in this work. The concept of $$\mu $$ μ -statistical convergence at infinity is also considered and the relationship between these two concepts is established. The concept of $$\mu \left[ p\right] $$ μ p -strong convergence at infinity point, generated by the measure $$\mu \left( \cdot \right) $$ μ · 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.