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.  

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.

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