An analysis of the convergence problem of a function in Sobolev and generalized Zygmund norms using product operator

In this paper, we delve into the convergence challenges concerning a function f represented as a Fourier series within Sobolev and generalized Zygmund norms. Our approach involves utilizing the deferred Nörlund–deferred Cesàro product ( $D_{h_{\mu}}^{d_{ \mu}}(N^{p,q})D_{g_{\mu}}^{h_{\mu}}(C)$ ) means of Fourier series in order to examine this convergence phenomenon. Further, we conduct a comparative analysis of the convergence outcomes through practical validations.