(On Summability Of Double Fourier Series By (N,p,q,p ́,q ́ )(E,1,1 - Karazon, Abdel Hadi Mohamed; Amer, Mohamed Mahmoud (Journal of natural sciences, life and applied sciences, 2018)
Let f be a function of two variables u,v, periodic with respect to u and with respect to v, in each case with period 2π, and summable in the square Q∶[-π,π]×[-π,π]. In this reserchewe will proof theorem. The first study summability of the Double Fourier series within a certain condition, and we put the necessary lemmas for this theorem by method (N,p,q,p ́,q ́ )(E,1,1). The objective of the research is to find a rough approximation of the series using two regular methods. Neither of the two methods can assign an approximate sum. In order to reach our desired goal, the analytical and synthetic method was adopted. We defined two regular Double methods and then applied them and applied the product to a known double series And a task commensurate with this task, and we can get many results, the most important of which is that the individual methods lead to the methods of the product and consistent with it, if we have a series can be summability in a single way, this series can also be summability to the same total plow And the opposite is not true in the general case, Knowing that the methods used and their products are regular. In conclusion, we can say that methods product are better able to collect the series than the methods themselves.