Quasi-Monotone Series

A generalization of quasi-monotone sequences

“…Theorem 3 provides an extension of the well known Cauchy condensation test for convergence. The extension of Cauchy's test for quasi-monotone sequences was proved by Shah (2) and Szasz (4).…”

Convergence of cauchy-riemann sums to cauchy-riemann integrals

“…The 1'e ult (2) has been generalized to the quasimonotone case by O. Szasz [6] and if the integral exists, then (1 ) holds. Kl'i hnan [9] has pointed out LhaL in cerLain (nonLrivial) cases a s tl'onger result than (1) is true, namely, (6) .1 0 for all sufficienLly small positive h ; ind eed :…”

“…Kl'i hnan [9] has pointed out LhaL in cerLain (nonLrivial) cases a s tl'onger result than (1) is true, namely, (6) .1 0 for all sufficienLly small positive h ; ind eed :…”

On weighted integrability of trigonometric series and 𝐿¹-convergence of Fourier series

“…For succinct formulation the «th partial sums of the Fourier series of / e Ll(0, it] are denoted Sn(f) = Sn(f, x). Also recall (Szasz [8]) that a null sequence {a(n)} is said to be quasi-monotone if, for some a > 0, a(n)/na J, for n 3* n0(a). An analogous result holds for sine series.…”