A Generalization of Monotonicity Condition And

It is well known that there are a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc.. Generally speaking, it has become an important topic how to generalize monotonicity. Recently, Leindler [5] defined a new class of sequences named as sequences of rest bounded variation and briefly denoted by RBV S, keeping some good properties of decreasing sequences. A null sequences C := {cn} is of rest bounded variation, or C ∈ RBV S, if cn → 0 and for any m ∈ N it holds that