Synchronal algorithm for a countable family of strict psedocontractions in q-uniformly smooth Banach spaces

2014 ◽  
Vol 8 ◽  
pp. 727-745
Author(s):  
Abba Auwalu
Keyword(s):  
Banach Spaces ◽  
Countable Family ◽  
Uniformly Smooth ◽  
Synchronal Algorithm ◽  
Uniformly Smooth Banach Spaces

scholarly journals Implicit Iterative Scheme for a Countable Family of Nonexpansive Mappings in 2-Uniformly Smooth Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Ming Tian ◽  
Xin Jin
Keyword(s):  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Continuous Operator ◽  
Countable Family ◽  
Uniformly Smooth ◽  
Mann Process ◽  
Uniformly Smooth Banach Spaces ◽  
Implicit Iterative Algorithm ◽  
Lipschitzian Continuous

Implicit Mann process and Halpern-type iteration have been extensively studied by many others. In this paper, in order to find a common fixed point of a countable family of nonexpansive mappings in the framework of Banach spaces, we propose a new implicit iterative algorithm related to a strongly accretive and Lipschitzian continuous operatorF:xn=αnγV(xn)+βnxn-1+((1-βn)I-αnμF)Tnxnand get strong convergence under some mild assumptions. Our results improve and extend the corresponding conclusions announced by many others.

MODIFIED HALPERN ITERATIVE ALGORITHM FOR NONEXPANSIVE MAPPINGS II

2011 ◽  
Vol 04 (04) ◽  
pp. 683-694
Author(s):  
Mengistu Goa Sangago
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Convergence Conditions ◽  
Uniformly Smooth ◽  
Additional Control ◽  
Uniformly Smooth Banach Spaces

Halpern iterative algorithm is one of the most cited in the literature of approximation of fixed points of nonexpansive mappings. Different authors modified this iterative algorithm in Banach spaces to approximate fixed points of nonexpansive mappings. One of which is Yao et al. [16] modification of Halpern iterative algorithm for nonexpansive mappings in uniformly smooth Banach spaces. Unfortunately, some deficiencies are found in the Yao et al. [16] control conditions imposed on the modified iteration to obtain strong convergence. In this paper, counterexamples are constructed to prove that the strong convergence conditions of Yao et al. [16] are not sufficient and it is also proved that with some additional control conditions on the parameters strong convergence of the iteration is obtained.

scholarly journals EQUILATERAL SETS IN UNIFORMLY SMOOTH BANACH SPACES

Mathematika ◽  
2014 ◽  
Vol 60 (1) ◽  
pp. 219-231 ◽  
Author(s):  
D. Freeman ◽  
E. Odell ◽  
B. Sari ◽  
Th. Schlumprecht
Keyword(s):  
Banach Spaces ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces ◽  
Equilateral Sets

scholarly journals Inertial Krasnoselskii–Mann Method in Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 638
Author(s):  
Yekini Shehu ◽  
Aviv Gibali
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Splitting Method ◽  
Uniformly Convex ◽  
Inclusion Problems ◽  
Uniformly Smooth ◽  
Mann Algorithm ◽  
Uniformly Smooth Banach Spaces

In this paper, we give a general inertial Krasnoselskii–Mann algorithm for solving inclusion problems in Banach Spaces. First, we establish a weak convergence in real uniformly convex and q-uniformly smooth Banach spaces for finding fixed points of nonexpansive mappings. Then, a strong convergence is obtained for the inertial generalized forward-backward splitting method for the inclusion. Our results extend many recent and related results obtained in real Hilbert spaces.

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