Convergence of Cesáro means with variable parameters of Walsh-Fourier series

Abstract

This Dissertation talks about convergence of Cesáro means with variable parameters for Walsh-Fourier series. we present some important and well-known notions and definitions related to the new results appearing in the thesis where we introduced the notion of Cesáro means of Fourier series with variable parameters. And we proved the almost everywhere convergence of a subsequnce of the Cesáro (C , α2n) means of integrable functions. And we introduced the notion of Cesáro means of Fourier series with variable parameters. We proved the almost everywhere convergence of the Cesáro (C , αn) means of integrable functions. And we formulated and proved that the maximal operator of some (C , βn) means of cubical partial sums of two variable Walsh-Fourier series of integrable functions is of weak type (L1,L1).