scholarly journals The alternating algorithm in a uniformly convex and uniformly smooth Banach space

2015 ◽  
Vol 421 (1) ◽  
pp. 747-753 ◽  
Author(s):  
Allan Pinkus
Keyword(s):  
Banach Space ◽  
Smooth Banach Space ◽  
Uniformly Convex ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth

The Extent of the Sequence Space Associated with a Basis

1972 ◽  
Vol 24 (4) ◽  
pp. 636-641 ◽  
Author(s):  
William H. Ruckle
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Smooth Banach Space ◽  
Uniformly Convex ◽  
Primary Motivation ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth ◽  
Recent Theorem

The associated sequence space S of a sequence of vectors {xn} in a Banach space consists of all scalar sequences (sn) for which converges. My primary motivation in writing this paper was to present a new proof to a recent theorem of N. I. and V. I. Gurarii concerning limits of extent on S when {xn} is a basis of a uniformly convex or a uniformly smooth Banach space [5], This theorem is stated as Theorem 2.4. Several interesting consequences of this theorem were noted by N. I. Gurarii in [3] and [4].

scholarly journals Local solvability of a constrainedgradient system of total variation

2003 ◽  
Vol 2003 (6) ◽  
pp. 353-365 ◽  
Author(s):  
C. E. Chidume ◽  
H. Zegeye
Keyword(s):  
Banach Space ◽  
Iterative Methods ◽  
Total Variation ◽  
Local Solvability ◽  
Independent Interest ◽  
Smooth Banach Space ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth ◽  
Compact Subsets

SupposeXis a realq-uniformly smooth Banach space andF,K:X→XwithD(K)=F(X)=Xare accretive maps. Under various continuity assumptions onFandKsuch that0=u+KFuhas a solution, iterative methods which converge strongly to such a solution are constructed. No invertibility assumption is imposed onKand the operatorsKandFneed not be defined on compact subsets ofX. Our method of proof is of independent interest.

Iterative Methods for Strictly Pseudo-Contractive Mappings

2013 ◽  
Vol 333-335 ◽  
pp. 1402-1405
Author(s):  
Yang Liu ◽  
Yan Hao
Keyword(s):  
Banach Space ◽  
Iterative Method ◽  
Strong Convergence ◽  
Iterative Methods ◽  
Smooth Banach Space ◽  
Convergence Theorems ◽  
Uniformly Smooth Banach Space ◽  
Contractive Mappings ◽  
Uniformly Smooth

The aim of this work is to consider an iterative method for a-strict pseudo-contractions. Strong convergence theorems are established in a real 2-uniformly smooth Banach space.

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