On Summability with a Rate of Spliced Sequences

Given a positive nonincreasing sequence \(\lambda=\left(\lambda_{n}\right)\) , we deal with the summability with a rate of \(o\left(\lambda_{n}\right)\) of spliced sequences formed by bounded sequences, and we obtain a bounding interval for \(\mathcal{K}\) -core of the \(T\) -transform of the spliced sequence \(x\) with a rate of \(o\left(\lambda_{n}\right)\) . In addition, we provide some inequalities for the limit superior and inferior of the \(T\) -transform with a rate of \(o\left(\lambda_{n}\right)\) of any bounded infinite splice via Lebesgue integral.