scholarly journals Convergence Theorems on a New Iteration Process for Two Asymptotically Nonexpansive Nonself-Mappings with Errors in Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-19
Author(s):  
Murat Ozdemir ◽  
Sezgin Akbulut ◽  
Hukmi Kiziltunc
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Scheme ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive

We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al. (2003), Wang (2006), Shahzad (2005), and Thianwan (2008).

scholarly journals Common Fixed Points for Weak and Strong Convergence Results

2016 ◽  
Vol 4 (2) ◽  
pp. 340
Author(s):  
S. C. Shrivastava
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Results

<div><p> <em>In this paper, we study the approximation of common fixed points for more general classes of mappings through weak and strong convergence results of an iterative scheme in a uniformly convex Banach space. Our results extend and improve some known recent results.</em></p></div>

scholarly journals Weak and strong convergence to fixed points of asymptotically nonexpansive mappings

1991 ◽  
Vol 43 (1) ◽  
pp. 153-159 ◽  
Author(s):  
J. Schu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive ◽  
Fourth Kind

Let T be an asymptotically nonexpansive self-mapping of a closed bounded and convex subset of a uniformly convex Banach space which satisfies Opial's condition. It is shown that, under certain assumptions, the sequence given by xn+1 = αnTn(xn) + (1 - αn)xn converges weakly to some fixed point of T. In arbitrary uniformly convex Banach spaces similar results are obtained concerning the strong convergence of (xn) to a fixed point of T, provided T possesses a compact iterate or satisfies a Frum-Ketkov condition of the fourth kind.

scholarly journals Strong convergence theorems of three-step iterations for multi-valued mappings in Banach spaces

Filomat ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 173-184
Author(s):  
S. Homaeipour ◽  
A. Razani
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Convergence Theorems

In this paper, two classes of three-step iteration schemes for multi-valued mappings in a uniformly convex Banach space are presented. Moreover, their strong convergence are proved.

scholarly journals Approximating Fixed Points of Operators Satisfying (RCSC) Condition in Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel de la Sen ◽  
Junaid Khan
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Nonempty Subset ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Numerical Efficiency

Let K be a nonempty subset of a Banach space E. A mapping T:K→K is said to satisfy (RCSC) condition if each a,b∈K, 1/2a−Fa≤a−b⇒Fa−Fb≤1/3a−b+a−Fb+b−Fa. In this paper, we study, under some appropriate conditions, weak and strong convergence for this class of maps through M iterates in uniformly convex Banach space. We also present a new example of mappings with condition (RCSC). We connect M iteration and other well-known processes with this example to show the numerical efficiency of our results. The presented results improve and extend the corresponding results of the literature.

scholarly journals Convergence theorems of finite-step iteration with errors for non-self asymptotically nonexpansive in the intermediate sense mappings

Filomat ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 81-103
Author(s):  
G.S. Saluja
Keyword(s):  
Banach Space ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Finite Step ◽  
Nonexpansive Retract ◽  
Bounded Sequences

Let K be a nonempty closed convex nonexpansive retract of a uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K ? E be non-self asymptotically nonexpansive in the intermediate sense mapping with F(T) = ?. Let {?ni}, {?ni} and {?ni} are sequences in [0, 1] with ?n(i) + ?n(i) + ?n(i) = 1 for all i = 1, 2, . . . , N. From arbitrary x1 ? K , define the sequence {xn } iteratively by (8), where {u(i) } for all i = 1, 2, . . . , N are bounded sequences in K with P? u(i) < ?. (i) If the dual E

scholarly journals Fixed points of mappings satisfying semicontractivity conditions

1992 ◽  
Vol 53 (1) ◽  
pp. 25-38
Author(s):  
Jürgen Schu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Convex Subset ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Opial’S Condition ◽  
Asymptotically Nonexpansive

AbstractLet A be a subset of a Banach space E. A mapping T: A →A is called asymptoically semicontractive if there exists a mapping S: A×A→A and a sequence (kn) in [1, ∞] such that Tx=S(x, x) for all x ∈A while for each fixed x ∈A, S(., x) is asymptotically nonexpansive with sequence (kn) and S(x,.) is strongly compact. Among other things, it is proved that each asymptotically semicontractive self-mpping T of a closed bounded and convex subset A of a uniformly convex Banach space E which satisfies Opial's condition has a fixed point in A, provided s has a certain asymptoticregurity property.

scholarly journals Convergence of Common Random Fixed Point of Finite Family of Asymptotically Quasi-Nonexpansive-Type Mappings by an Implicit Random Iterative Scheme

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
A. S. Saluja ◽  
Pankaj kumar Jhade
Keyword(s):  
Banach Space ◽  
Iterative Scheme ◽  
Sufficient Conditions ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Finite Family ◽  
Uniformly Convex ◽  
Random Fixed Point ◽  
Random Iteration ◽  
Necessary And Sufficient

We introduce a new implicit random iteration process generated by a finite family of asymptotically quasi-nonexpansive-type mappings and study necessary and sufficient conditions for the convergence of this process in a uniformly convex Banach space. The results presented in this paper extend and improve the recent ones announced by Plubtieng et al. (2007), Beg and Thakur (2009), and Saluja and Nashine (2012).

scholarly journals Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-19
Author(s):  
Tanakit Thianwan
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Iteration Scheme ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Ishikawa Iteration ◽  
Asymptotically Nonexpansive ◽  
Differentiable Norm ◽  
Fréchet Differentiable

We study weak convergence of the projection type Ishikawa iteration scheme for two asymptotically nonexpansive nonself-mappings in a real uniformly convex Banach spaceEwhich has a Fréchet differentiable norm or its dualE*has the Kadec-Klee property. Moreover, weak convergence of projection type Ishikawa iterates of two asymptotically nonexpansive nonself-mappings without any condition on the rate of convergence associated with the two maps in a uniformly convex Banach space is established. Weak convergence theorem without making use of any of the Opial's condition, Kadec-Klee property, or Fréchet differentiable norm is proved. Some results have been obtained which generalize and unify many important known results in recent literature.

scholarly journals Hybrid Implicit Iteration Process for a Finite Family of Non-Self-Nonexpansive Mappings in Uniformly Convex Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Qiaohong Jiang ◽  
Jinghai Wang ◽  
Jianhua Huang
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Uniformly Convex Banach Spaces ◽  
Implicit Iteration

Weak and strong convergence theorems are established for hybrid implicit iteration for a finite family of non-self-nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results.

Sign in / Sign up

Export Citation Format

Share Document