scholarly journals Convergence Analysis for a Three-Step Thakur Iteration for Suzuki-Type Nonexpansive Mappings with Visualization

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1441 ◽  
Author(s):  
Gabriela Ioana Usurelu ◽  
Mihai Postolache
Keyword(s):  
Banach Space ◽  
Numerical Experiment ◽  
Convergence Analysis ◽  
Normed Space ◽  
Visual Analysis ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Topological Properties

The class of Suzuki mappings is reanalyzed in connection with a three-steps Thakur procedure. The setting is provided by a uniformly convex Banach space, that is normed space endowed with some symmetric geometric properties and some topological properties. Once more, the fact that property ( C ) holds on as a generalized nonexpansiveness condition is emphasized throughout some examples. One example uses the setting of R 2 with the Taxicab norm. It is further included in a numerical experiment in connection with seven iteration procedures, resulting a visual analysis of convergence.

scholarly journals Approximating fixed points by ishikawa iterates

1989 ◽  
Vol 40 (1) ◽  
pp. 113-117 ◽  
Author(s):  
M. Maiti ◽  
M.K. Ghosh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex

In a uniformly convex Banach space the convergence of Ishikawa iterates to a fixed point is discussed for nonexpansive and generalised nonexpansive mappings.

scholarly journals Convergence results of a faster iterative scheme including multi-valued mappings in Banach spaces

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1359-1368
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Muhammad Khan ◽  
Naseer Muhammad
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Current Literature ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Numerical Efficiency ◽  
Convergence Results

In this paper, we study M-iterative scheme in the new context of multi-valued generalized ?-nonexpansive mappings. A uniformly convex Banach space is used as underlying setting for our approach. We also provide a new example of generalized ?-nonexpasive mappings. We connect M iterative scheme and other well known schemes with this example, to show the numerical efficiency of our results. Our results improve and extend many existing results in the current literature.

scholarly journals Ishikawa iteration process with errors for nonexpansive mappings in uniformly convex Banach spaces

2000 ◽  
Vol 24 (1) ◽  
pp. 49-53 ◽  
Author(s):  
Deng Lei ◽  
Li Shenghong
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Ishikawa Iteration ◽  
Uniformly Convex Banach Spaces ◽  
Ishikawa Iteration Process

We shall consider the behaviour of Ishikawa iteration with errors in a uniformly convex Banach space. Then we generalize the two theorems of Tan and Xu without the restrictions thatCis bounded andlimsupnsn<1.

scholarly journals Composite Iterative Algorithms for Variational Inequality and Fixed Point Problems in Real Smooth and Uniformly Convex Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Point Problem ◽  
Uniformly Convex ◽  
Differentiable Norm

We introduce composite implicit and explicit iterative algorithms for solving a general system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in a real smooth and uniformly convex Banach space. These composite iterative algorithms are based on Korpelevich's extragradient method and viscosity approximation method. We first consider and analyze a composite implicit iterative algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another composite explicit iterative algorithm in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm. Under suitable assumptions, we derive some strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literatures.

scholarly journals Approximating fixed points of nonexpansive and generalized nonexpansive mappings

1993 ◽  
Vol 16 (1) ◽  
pp. 81-86 ◽  
Author(s):  
M. Maiti ◽  
B. Saha
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex

In this paper we consider a mappingSof the formS=α0I+α1T+α2T2+…+αKTK, whereαi≥0.α1>0with∑i=0kαi=1, and show that in a uniformly convex Banach space the Picard iterates ofSconverge to a fixed point ofTwhenTis nonexpansive or generalized nonexpansive or even quasinonexpansive.

scholarly journals Estimation of Newly Established Iterative Scheme for Generalized Nonexpansive Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Aftab Hussain ◽  
Nawab Hussain ◽  
Danish Ali
Keyword(s):  
Banach Space ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Space Environment ◽  
Iterative Approach ◽  
Uniformly Convex ◽  
Prior Art ◽  
Nonexpansive Maps ◽  
New Iterative Method

We introduce a new iterative method in this article, called the D iterative approach for fixed point approximation. Analytically, and also numerically, we demonstrate that our established D I.P is faster than the well-known I.P of the prior art. Finally, in a uniformly convex Banach space environment, we present weak as well as strong convergence theorems for Suzuki’s generalized nonexpansive maps. Our findings are an extension, refinement, and induction of several existing iterative literatures.

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 Weak convergence theorem for Passty type asymptotically nonexpansive mappings

1999 ◽  
Vol 22 (1) ◽  
pp. 217-220
Author(s):  
B. K. Sharma ◽  
B. S. Thakur ◽  
Y. J. Cho
Keyword(s):  
Banach Space ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Differentiable Norm ◽  
Weak Convergence Theorem ◽  
Fréchet Differentiable

In this paper, we prove a convergence theorem for Passty type asymptotically nonexpansive mappings in a uniformly convex Banach space with Fréchet-differentiable norm.

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