The effects of matrix summability methodson bounds of function sequences Original Research Article

Agnew characterized the triangular regular matrices for which the inequality limsupG(Aℱ;D)≤limsupG(ℱ;D)limsupG(Aℱ;D)≤limsupG(ℱ;D) Turn MathJax on holds, where G(ℱ D) denotes the least upper bound of the element fn(χ) of the function sequence.ℱ := (fn) over the subset D of real numbers and Aℱ :=(Afn) is given by View the MathML sourceAfn(x):=∑k=1∞ankfk(x). Turn MathJax on Replacing lim sup operator by stT-lim sup operator, we prove some variants of Agnewʹs result.