scholarly journals Strong convergence of modified Noor iterations

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Yongfu Su ◽  
Xiaolong Qin
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Strong Convergence Theorem ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces

In this paper, strong convergence theorem is obtained for the modified Noor iterations in the framework of uniformly smooth Banach spaces. Our results extend and improve the recent ones announced by Wittman, Kim, Xu, and some others.

scholarly journals Strong Convergence Theorems of Modified Ishikawa Iterative Method for an Infinite Family of Strict Pseudocontractions in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
Phayap Katchang ◽  
Wiyada Kumam ◽  
Usa Humphries ◽  
Poom Kumam
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Infinite Family ◽  
Strong Convergence Theorem ◽  
Mild Conditions ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces ◽  
Ishikawa Iterative Process

We introduce a new modified Ishikawa iterative process and a new W-mapping for computing fixed points of an infinite family of strict pseudocontractions mapping in the framework of q-uniformly smooth Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions. The results obtained in this paper extend and improve the recent results of Cai and Hu 2010, Dong et al. 2010, Katchang and Kumam 2011 and many others in the literature.

Strong convergence theorem for fixed points of relatively nonexpansive multi-valued mappings and equilibrium problems in Banach spaces

2020 ◽  
pp. 2150137
Author(s):  
Adeolu Taiwo ◽  
Timilehin Opeyemi Alakoya ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Fixed Point Set ◽  
Computational Performance ◽  
Relatively Nonexpansive ◽  
Point Set ◽  
Uniformly Smooth Banach Spaces

In this paper, we study the problem of finding a common element of the solution set of monotone equilibrium problem and the fixed point set of relatively nonexpansive multi-valued mappings in uniformly convex and uniformly smooth Banach spaces. We introduce a Halpern-S-iteration for solving the problem and establish a strong convergence theorem. Some consequences and applications of our main results are discussed. Some numerical experiments are performed to illustrate the convergence and computational performance of our algorithm in comparison with others having similar features. The numerical results have confirmed that the proposed algorithm has a competitive advantage over the existing methods. Our results extend and generalize some results in the literature in this direction.

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.

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 Strong Convergence Theorems for Families of Weak Relatively Nonexpansive Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-19
Author(s):  
Yekini Shehu
Keyword(s):  
Strong Convergence ◽  
Convergence Theorem ◽  
Real Banach Space ◽  
Hybrid Methods ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Relatively Nonexpansive Mappings ◽  
Uniformly Smooth ◽  
Relatively Nonexpansive

We construct a new Halpern type iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space using the properties of generalizedf-projection operator. Using this result, we discuss strong convergence theorem concerning generalH-monotone mappings. Our results extend many known recent results in the literature.

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