An Analysis of the Convergence Problem of a Function in Functional Norms by Applying the Generalized Nörlund-Matrix Product Operator

Abstract

In this paper, we analyze the convergence problems of function g of Fourier series in Besov and generalized Zygmund norms using generalized Nörlund-Matrix (Np,qA) means of Fourier series. Convergence results are also compared by means of applications.

Keywords

• degree of convergence
• Besov space (B.S.)
• generalized Zygmund spaces (G.Z.S.)
• N p , q A ) operator%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> generalized Nörlund-Matrix (<named-content content-type="inline-formula"><inline-formula> <mml:math id="mm999"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>N</mml:mi> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:msup> <mml:mi>A</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>) operator
• Fourier series (F.S.)