scholarly journals A Note on the Strong Convergence of Partial Sums with Respect to Vilenkin System

2019 ◽  
Vol 54 (6) ◽  
pp. 365-370
Author(s):  
G. Tutberidze
Keyword(s):  
Strong Convergence ◽  
Partial Sums ◽  
Vilenkin System

scholarly journals Some new resuts concering strong convergence of Fejér means with respect to Vilenkin systems

2021 ◽  
Vol 73 (4) ◽  
pp. 544-555
Author(s):  
G. Tutberidze ◽  
L.-E. Persson ◽  
G. Tephnadze ◽  
P. Wall
Keyword(s):  
Strong Convergence ◽  
Partial Sums ◽  
Convergence Theorems ◽  
Vilenkin System ◽  
Fejér Means

UDC 517.5 We prove some new strong convergence theorems for partial sums and Fej\'er means with respect to the Vilenkin system.  

scholarly journals Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Xueping Hu ◽  
Guohua Fang ◽  
Dongjin Zhu
Keyword(s):  
Strong Convergence ◽  
Convergence Property ◽  
Random Sequence ◽  
Weighted Sums ◽  
Partial Sums ◽  
Moment Inequality ◽  
Convergence Properties ◽  
Negatively Associated ◽  
The Moment ◽  
Asymptotically Almost Negatively Associated

By applying the moment inequality for asymptotically almost negatively associated (in shortAANA) random sequence and truncated method, we get the three series theorems forAANArandom variables. Moreover, a strong convergence property for the partial sums ofAANArandom sequence is obtained. In addition, we also study strong convergence property for weighted sums ofAANArandom sequence.

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

scholarly journals Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Error Bounds ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Dirichlet Kernel ◽  
Partial Sums ◽  
Functions Of Bounded Variation ◽  
Moduli Of Continuity ◽  
Fourier Approximation

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.

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