Convergence Theorems of a Finite-Step Iteration Algorithm Under Two Finite Families of Total Asymptotically Quasi-Nonexpansive Maps

2018 ◽  
Author(s):  
Salwa Salman Abed ◽  
Zahra Mahmood Mohamed Hasan
Keyword(s):  
Iteration Algorithm ◽  
Convergence Theorems ◽  
Nonexpansive Maps ◽  
Finite Step

scholarly journals Common Fixed Point of a Finite-step Iteration Algorithm Under Total Asymptotically Quasi-nonexpansive Maps

2019 ◽  
Vol 16 (3) ◽  
pp. 0654
Author(s):  
Abed Et al.
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Convex Banach Space ◽  
Finite Family ◽  
Iteration Algorithm ◽  
Uniformly Convex ◽  
Nonexpansive Maps ◽  
Finite Step

      Throughout this paper, a generic iteration algorithm for a finite family of total asymptotically quasi-nonexpansive maps in uniformly convex Banach space is suggested. As well as weak / strong convergence theorems of this algorithm to a common fixed point are established. Finally, illustrative numerical example by using Matlab is presented.

scholarly journals A one-step-two-mappings iterative scheme for multi-valued maps in W-hyperbolic spaces

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1403-1411 ◽  
Author(s):  
Birol Gunduz ◽  
Sezgin Akbulut
Keyword(s):  
Banach Spaces ◽  
Hyperbolic Space ◽  
Iterative Scheme ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Nonexpansive Maps ◽  
Uniformly Convex Banach Spaces ◽  
One Step ◽  
Geodesic Spaces

In this paper, we study a one-step iterative scheme for two multi-valued nonexpansive maps in W-hyperbolic spaces. We establish strong and ?-convergence theorems for the proposed algorithm in a uniformly convex W-hyperbolic space which improve and extend the corresponding known results in uniformly convex Banach spaces as well as CAT(0) spaces. Our new results are also valid in geodesic spaces.

scholarly journals A path convergence theorem and construction of fixed points for nonexpansive mappings in certain Banach spaces

2016 ◽  
Vol 32 (2) ◽  
pp. 241-250
Author(s):  
T. M. M. SOW ◽  
◽  
N. DJITTE ◽  
C.E. CHIDUME ◽  
◽  
...  
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Nonexpansive Maps ◽  
Weakly Continuous ◽  
Duality Map

In this paper, we introduce a new iterative process to approximate fixed points of nonexpansive maps in real Banach spaces having weakly continuous duality map and establish strong convergence theorems for the proposed iterative process. There is no compactness assumption on K or on T. Our results improve important recent results.

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 Weak and Strong Convergence Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lei Deng ◽  
Juan Xiao
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Iteration Sequence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Finite Step

A finite-step iteration sequence for two finite families of asymptotically nonexpansive mappings is introduced and the weak and strong convergence theorems are proved in Banach space. The results presented in the paper generalize and unify some important known results of relevant scholars.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

STRONG AND Δ - CONVERGENCE THEOREMS USING MODIFIED PROXIMAL POINT ALGORITHM IN CAT(0) SPACES

2018 ◽  
Vol 7 (2) ◽  
pp. 8
Author(s):  
KUMAR DAS APURVA ◽  
DHAR DIWAN SHAILESH ◽  
DASHPUTRE SAMIR ◽  
◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Convergence Theorems
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