Regular statistical convergence of multiple sequences
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Ferenc Móricz
Abstract
The concepts of statistical convergence of single and multiple sequences of complex numbers were introduced in [2] and [8], respectively. In this paper, we introduce the concept indicated in the title. We prove that if a d-multiple sequence is regularly statistically convergent, then its statistical limit can be computed as the iterated statistical limit of the statistical limits of its subsequences which correspond to an arbitrary partition of the index set {1,2,..., d}, d ≥ 2. As an application, we prove that if a function ƒ is in Lp(Td) for some p > 1, T = [0, 2π), then the (symmetric) rectangular partial sums of its d-multiple Fourier series are regularly statistically convergent to ƒ { u1, . . . , ud) at almost every point (u1,..., ud) ∈Td. Furthermore, if ƒ is in C(Td), then the regular statistical convergence of the rectangular partial sums takes place uniformly on Td.
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Articles in the same Issue
- Masthead
- A nonlinear-stability analysis of second-order fluid in porous medium in presence of magnetic field
- Convergence rate for some additive function on random permutations
- The converse of the Fabry-Pólya theorem on singularities of lacunary power series
- On meromorphic functions that share one value with their derivative
- Interrelations Between the Taylor Coefficients of a Matricial Carathéodory Function and Its Cayley Transform
- Domains of uniform convergence of real rational chebyshev approximants
- Regular statistical convergence of multiple sequences
