A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces

1997 ◽  
Vol 32 (2) ◽  
pp. 167-174 ◽  
Author(s):  
André Adler ◽  
Andrew Rosalsky ◽  
Andrej I. Volodin
Keyword(s):  
Banach Spaces ◽  
Convergence Theorem ◽  
Mean Convergence ◽  
Random Elements

scholarly journals Mean convergence theorem for multidimensional arrays of random elements in Banach spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-6
Author(s):  
Le Van Thanh
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Multidimensional Arrays ◽  
Stable Type ◽  
Dimensional Array ◽  
Mean Convergence ◽  
Random Elements ◽  
Convergence In Mean

For a d-dimensional array of random elements {Vn,n∈ℤ+d} in a real separable stable type p (1≤p<2) Banach space, a mean convergence theorem is established. Moreover, the conditions for the convergence in mean of order p are shown to completely characterize stable-type p Banach spaces.

scholarly journals Extending the Applicability of a Two-Step Chord-Type Method for Non-Differentiable Operators

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 804
Author(s):  
Ioannis K. Argyros ◽  
Neha Gupta ◽  
J. P. Jaiswal
Keyword(s):  
Approximate Solution ◽  
Convergence Analysis ◽  
Banach Spaces ◽  
Recurrence Relation ◽  
Convergence Theorem ◽  
Local Convergence ◽  
Existence And Uniqueness ◽  
Numerical Illustration ◽  
Type Method ◽  
Local Convergence Analysis

The semi-local convergence analysis of a well defined and efficient two-step Chord-type method in Banach spaces is presented in this study. The recurrence relation technique is used under some weak assumptions. The pertinency of the assumed method is extended for nonlinear non-differentiable operators. The convergence theorem is also established to show the existence and uniqueness of the approximate solution. A numerical illustration is quoted to certify the theoretical part which shows that earlier studies fail if the function is non-differentiable.

Some mean convergence theorems for weighted sums of Banach space valued random elements

Stochastics ◽  
2021 ◽  
pp. 1-19
Author(s):  
Pingyan Chen ◽  
Manuel Ordóñez Cabrera ◽  
Andrew Rosalsky ◽  
Andrei Volodin
Keyword(s):  
Banach Space ◽  
Weighted Sums ◽  
Convergence Theorems ◽  
Mean Convergence ◽  
Random Elements

scholarly journals A Strong Convergence Theorem for Relatively Nonexpansive Mappings and Equilibrium Problems in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Mei Yuan ◽  
Xi Li ◽  
Xue-song Li ◽  
John J. Liu
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Projection Method ◽  
Convergence Theorem ◽  
Projection Operator ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

Relatively nonexpansive mappings and equilibrium problems are considered based on a shrinking projection method. Using properties of the generalizedf-projection operator, a strong convergence theorem for relatively nonexpansive mappings and equilibrium problems is proved in Banach spaces under some suitable conditions.

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