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 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 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 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 COMMON FIXED POINTS FOR SEMIGROUPS OF POINTWISE LIPSCHITZIAN MAPPINGS IN BANACH SPACES

2011 ◽  
Vol 84 (3) ◽  
pp. 353-361 ◽  
Author(s):  
W. M. KOZLOWSKI
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Banach Spaces ◽  
Convex Subset ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Lipschitzian Mappings ◽  
Nonlinear Mappings

AbstractLet C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the existence of common fixed points for pointwise Lipschitzian semigroups of nonlinear mappings Tt:C→C, where each Tt is pointwise Lipschitzian. The latter means that there exists a family of functions αt:C→[0,∞) such that $\|T_t(x)-T_t(y)\| \leq \alpha _{t}(x)\|x-y\|$ for x,y∈C. We also demonstrate how the asymptotic aspect of the pointwise Lipschitzian semigroups can be expressed in terms of the respective Fréchet derivatives.

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 Browder’s Convergence Theorem for Multivalued Mappings in Banach Spaces without the Endpoint Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Thanomsak Laokul
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Multivalued Mappings ◽  
Uniformly Convex ◽  
Uniformly Gâteaux Differentiable Norm ◽  
Differentiable Norm

We prove Browder’s convergence theorem for multivalued mappings in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm by using the notion of diametrically regular mappings. Our results are significant improvement on results of Jung (2007) and Panyanak and Suantai (2020).

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 p-Uniform Convexity andq-Uniform Smoothness of Absolute Normalized Norms onℂ2

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Tomonari Suzuki
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convex Banach Space ◽  
Uniform Convexity ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Uniform Smoothness

We first prove characterizations ofp-uniform convexity andq-uniform smoothness. We next give a formulation on absolute normalized norms onℂ2. Using these, we present some examples of Banach spaces. One of them is a uniformly convex Banach space which is notp-uniformly convex.

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 Approximating Common Fixed Points of Nonexpansive Mappings in Banach Spaces

2006 ◽  
Vol 13 (3) ◽  
pp. 529-537
Author(s):  
Naseer Shahzad ◽  
Reem Al-Dubiban
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Convex Subset ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence

Abstract Let 𝐾 be a nonempty closed convex subset of a real uniformly convex Banach space 𝐸 and 𝑆, 𝑇 : 𝐾 → 𝐾 two nonexpansive mappings such that 𝐹(𝑆) ∩ 𝐹(𝑇) := {𝑥 ∈ 𝐾 : 𝑆𝑥 = 𝑇𝑥 = 𝑥} ≠ ø. Suppose {𝑥𝑛} is generated iteratively by 𝑥1 ∈ 𝐾, 𝑥𝑛+1 = (1 – α 𝑛)𝑥𝑛 + α 𝑛𝑆[(1 – β 𝑛)𝑥𝑛 + β 𝑛𝑇𝑥𝑛], 𝑛 ≥ 1, where {α 𝑛}, {β 𝑛} are real sequences in [0, 1]. In this paper, we discuss the weak and strong convergence of {𝑥𝑛} to some 𝑥* ∈ 𝐹(𝑆) ∩ 𝐹(𝑇).

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