Approximation by matrix means of double Vilenkin-Fourier series

Abstract In the present paper, we discuss the rate of the approximation by the matrix transform of partial sums of double Vilenkin-Fourier series in L p ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mtable columnalign="center" rowspacing="4pt" columnspacing="1em"> <m:mtr> <m:mtd> <m:mstyle displaystyle="true"> <m:msubsup> <m:mi>G</m:mi> <m:mrow class="MJX-TeXAtom-ORD"> <m:mi>m</m:mi> </m:mrow> <m:mrow class="MJX-TeXAtom-ORD"> <m:mn>2</m:mn> </m:mrow> </m:msubsup> </m:mstyle> </m:mtd> </m:mtr> </m:mtable> </m:math> $\begin{array}{} \displaystyle G_{m}^{2} \end{array}$ ) space (1 ≤ p &lt; ∞) and in C ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mtable columnalign="center" rowspacing="4pt" columnspacing="1em"> <m:mtr> <m:mtd> <m:mstyle displaystyle="true"> <m:msubsup> <m:mi>G</m:mi> <m:mrow class="MJX-TeXAtom-ORD"> <m:mi>m</m:mi> </m:mrow> <m:mrow class="MJX-TeXAtom-ORD"> <m:mn>2</m:mn> </m:mrow> </m:msubsup> </m:mstyle> </m:mtd> </m:mtr> </m:mtable> </m:math> $\begin{array}{} \displaystyle G_{m}^{2} \end{array}$ ). We give an application for Lipschitz functions.