scholarly journals Approximating Fixed Points of Bregman Generalized α-Nonexpansive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 709 ◽  
Author(s):  
Kanikar Muangchoo ◽  
Poom Kumam ◽  
Yeol Je Cho ◽  
Sompomg Dhompongsa ◽  
Sakulbuth Ekvittayaniphon
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Iterative Schemes ◽  
Numerical Example ◽  
New Class

In this paper, we introduce a new class of Bregman generalized α -nonexpansive mappings in terms of the Bregman distance. We establish several weak and strong convergence theorems of the Ishikawa and Noor iterative schemes for Bregman generalized α -nonexpansive mappings in Banach spaces. A numerical example is given to illustrate the main results of fixed point approximation using Halpern’s algorithm.

scholarly journals Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Convergence Theorems ◽  
Numerical Example

In this paper, we propose the generalized M-iteration process for approximating the fixed points from Banach spaces to hyperbolic spaces. Using our new iteration process, we prove Δ-convergence and strong convergence theorems for the class of mappings satisfying the condition Cλ and the condition E which is the generalization of Suzuki generalized nonexpansive mappings in the setting of hyperbolic spaces. Moreover, a numerical example is given to present the capability of our iteration process and the solution of the integral equation is also illustrated using our main result.

scholarly journals Weak and strong convergence theorems for three Suzuki’s generalized nonexpansive mappings

2021 ◽  
Vol 110 (124) ◽  
pp. 121-129
Author(s):  
Seyit Temir
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems

We introduce a new iterative scheme for finding a common fixed point of three Suzuki?s generalized nonexpansive mappings in Banach spaces. We establish weak and strong convergence theorems for three Suzuki?s generalized nonexpansive mappings. The results obtained extend and improve the recent ones announced by Ali et al., Maniu and Thakur et al..

scholarly journals Convergence of CR-iteration to common fixed points of three g-nonexpansive mappings in Banach spaces with graphs

2019 ◽  
Vol 16 (3) ◽  
pp. 76
Author(s):  
Nguyen Trung Hieu ◽  
Pham Thi Ngoc Mai
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Numerical Example

The research introduces CR-iteration process and establishes some results about the weak and strong convergence of CR-iteration process to common fixed points of three G-nonexpansive mappings in uniformly convexBanach spaces with graphs. In addition, a numerical example is provided to illustrate for the convergence of CR-iteration process to common fixed points three G-nonexpansive mappings.

scholarly journals On Reich type λ−α-nonexpansive mapping in Banach spaces with applications to L1([0,1])

2018 ◽  
Vol 19 (2) ◽  
pp. 291
Author(s):  
Rabah Belbaki ◽  
E. Karapinar ◽  
Amar Ould-Hammouda,
Keyword(s):  
Banach Space ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Partial Order ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
New Class ◽  
Krasnoselskii Iteration

<p>In this manuscript we introduce a new class of monotone generalized nonexpansive mappings and establish some weak and strong convergence theorems for Krasnoselskii iteration in the setting of a Banach space with partial order. We consider also an application to the space L<sub>1</sub>([0,1]). Our results generalize and unify the several related results in the literature.</p>

Some convergence results of M iterative process in Banach spaces

2019 ◽  
pp. 2150017 ◽  
Author(s):  
Kifayat Ullah ◽  
Faiza Ayaz ◽  
Junaid Ahmad
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Weak And Strong Convergence ◽  
Convergence Results

In this paper, we prove some weak and strong convergence results for generalized [Formula: see text]-nonexpansive mappings using [Formula: see text] iteration process in the framework of Banach spaces. This generalizes former results proved by Ullah and Arshad [Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process, Filomat 32(1) (2018) 187–196].

scholarly journals Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings

2004 ◽  
Vol 2004 (37) ◽  
pp. 1965-1971 ◽  
Author(s):  
Hafiz Fukhar-ud-din ◽  
Safeer Hussain Khan
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
The Common

A two-step iterative scheme with errors has been studied to approximate the common fixed points of two asymptotically nonexpansive mappings through weak and strong convergence in Banach spaces.

scholarly journals Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohammed Ali Alghamdi ◽  
Naseer Shahzad ◽  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Finite Family ◽  
Monotone Mappings ◽  
Reflexive Banach Spaces ◽  
Convergence Theorems

We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

scholarly journals Convergence theorems for Bregman strongly nonexpansive mappings in reflexive Banach spaces

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1525-1536 ◽  
Author(s):  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Convergence Theorems

In this paper, we study a strong convergence theorem for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. As a consequence, we prove convergence theorem for a common fixed point of a finite family of Bergman relatively nonexpansive mappings. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common zero of a finite family of Bregman inverse strongly monotone mappings and a solution of a finite family of variational inequality problems.

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