Convergence of path and an iterative method for families of nonexpansive mappings

2008 ◽  
Vol 87 (1) ◽  
pp. 117-129 ◽  
Author(s):  
Charles Ejike Chidume ◽  
Bashir Ali
Keyword(s):  
Iterative Method ◽  
Nonexpansive Mappings

A general iterative method for an infinite family of nonexpansive mappings

2008 ◽  
Vol 69 (5-6) ◽  
pp. 1644-1654 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Rudong Chen
Keyword(s):  
Iterative Method ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
General Iterative Method

scholarly journals Steepest-descent Ishikawa iterative methods for a class of variational inequalities in Banach spaces

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1557-1569
Author(s):  
Nguyen Buong ◽  
Nguyen Anh ◽  
Khuat Binh
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Uniformly Smooth ◽  
Differentiable Norm ◽  
Strictly Convex Banach Spaces

In this paper, for finding a fixed point of a nonexpansive mapping in either uniformly smooth or reflexive and strictly convex Banach spaces with a uniformly G?teaux differentiable norm, we present a new explicit iterative method, based on a combination of the steepest-descent method with the Ishikawa iterative one. We also show its several particular cases one of which is the composite Halpern iterative method in literature. The explicit iterative method is also extended to the case of infinite family of nonexpansive mappings. Numerical experiments are given for illustration.

scholarly journals An iterative method for solving multiple-set split feasibility problems in Banach spaces

2020 ◽  
Vol 36 (1) ◽  
pp. 1-13
Author(s):  
SULIMAN AL-HOMIDAN ◽  
BASHIR ALI ◽  
YUSUF I. SULEIMAN
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Convergence Result ◽  
Uniformly Convex ◽  
Split Feasibility Problems ◽  
Uniformly Smooth ◽  
Convex Problem ◽  
Split Feasibility

"In this paper, we study generalized multiple-set split feasibility problems (in short, GMSSFP) in the frame workof p-uniformly convex real Banach spaces which are also uniformly smooth. We construct an iterative algo-rithm which is free from an operator norm and prove its strong convergence to a solution of GMSSFP, thatis, a solution of convex problem and a common fixed point of a countable family of Bregman asymptoticallyquasi-nonexpansive mappings without requirement for semi-compactness on the mappings. We illustrate ouralgorithm and convergence result by a numerical example. "

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