On Nörlund summability of double Fourier series

Abstract

In this research paper, the authors studied some problems related to harmonic summability of double Fourier series on Nörlund summability method. These results constitute substantial extension and generalization of related work of Moricz [<a href="#1">1</a>] and Rhodes <i>et al.</i>, [<a href="#2">2</a>]. We also constructed a new result on \((N,p^{(1)}_b,p^{(2)}_a)\) by regular Nörlund method of summability.

On a New Application of Positive and Decreasing Sequences to Double Fourier Series Associated with (N, p^(1)_m, p^(2)_n)

“…There are several results on summability by Nörlund means of Fourier series. The authors [2,4,6,7,9,13,14] have looked into it. This encourages us to research it in both more generalized and particular cases.…”

Critical Analyzing on Some New Application of Almost Decreasing Sequence to Legendre Series Associated with [B] Sum

“…Most eminent mathematical analysts have focused their creative energy on the theory of series. The late 19th and early 20th centuries are credited with being the eras when adequate methods were able to associate with them certain values that could be called their sums in a reasonable manner through a process closely associated with Cauchy's concept of convergence (see [13][14][15][16][17][18][19][20]). [11]); Consider a sequence { 𝑈 𝑚 } of 𝑚 𝑡ℎ partial sums corresponding to the infinite series ∑ 𝑢 𝑚 .…”