A new strong convergence Theorem for Lipschitzian strongly pseudocontractive Mappings in a real Banach space

2017 ◽  
Vol 41 (2) ◽  
pp. 205-209
Author(s):  
Ashish Nandal ◽  
Renu Chugh
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Real Banach Space ◽  
Strong Convergence Theorem ◽  
Pseudocontractive Mappings

scholarly journals Strong convergence theorem for two asymptotically quasi-nonexpansive mappings with errors in Banach space

2007 ◽  
Vol 38 (1) ◽  
pp. 85-92 ◽  
Author(s):  
G. S. Saluja
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Convex Subset ◽  
Convergence Theorem ◽  
Real Banach Space ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Strong Convergence Theorem

In this paper, we study strong convergence of common fixed points of two asymptotically quasi-nonexpansive mappings and prove that if $K$ is a nonempty closed convex subset of a real Banach space $E$ and let $ S, T\colon K\to K $ be two asymptotically quasi-nonexpansive mappings with sequences $ \{u_n\}$, $\{v_n\}\subset [0,\infty) $ such that $ \sum_{n=1}^{\infty}u_n

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.

scholarly journals A Strong Convergence Theorem for a Common Fixed Point of Two Sequences of Strictly Pseudocontractive Mappings in Hilbert Spaces and Applications

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Pseudocontractive Mappings ◽  
Strict Pseudocontraction ◽  
Strictly Pseudocontractive Mappings

We prove a strong convergence theorem for a common fixed point of two sequences of strictly pseudocontractive mappings in Hilbert spaces. We also provide some applications of the main theorem to find a common element of the set of fixed points of a strict pseudocontraction and the set of solutions of an equilibrium problem in Hilbert spaces. The results extend and improve the recent ones announced by Marino and Xu (2007) and others.

scholarly journals Strong Convergence for Hybrid ImplicitS-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shin Min Kang ◽  
Arif Rafiq ◽  
Faisal Ali ◽  
Young Chel Kwun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Real Banach Space ◽  
Iteration Scheme ◽  
Nonempty Closed Convex Subset ◽  
Pseudocontractive Mappings

LetKbe a nonempty closed convex subset of a real Banach spaceE, letS:K→Kbe nonexpansive, and let  T:K→Kbe Lipschitz strongly pseudocontractive mappings such thatp∈FS∩FT=x∈K:Sx=Tx=xandx-Sy≤Sx-Sy and x-Ty≤Tx-Tyfor allx, y∈K. Letβnbe a sequence in0, 1satisfying (i)∑n=1∞βn=∞; (ii)limn→∞⁡βn=0.For arbitraryx0∈K, letxnbe a sequence iteratively defined byxn=Syn, yn=1-βnxn-1+βnTxn, n≥1.Then the sequencexnconverges strongly to a common fixed pointpofSandT.

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