scholarly journals Weak and strong convergence results for the modified Noor iteration of three quasi-nonexpansive multivalued mappings in Hilbert spaces

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2495-2510
Author(s):  
Watcharaporn Chaolamjiak ◽  
Suhel Khan ◽  
Hasanen Hammad ◽  
Hemen Dutta
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Projection Methods ◽  
Iteration Scheme ◽  
Multivalued Mappings ◽  
Technical Term ◽  
Convergence Results ◽  
Comparison Results ◽  
Weak Convergence Theorem ◽  
Shrinking Projection Methods

The paper aims to present an advanced algorithm by taking help of the Noor-iteration scheme along with the inertial technical term for three quasi-nonexpansive multivalued in Hilbert spaces. A weak convergence theorem under certain conditions has been given and added the CQ and shrinking projection methods to our algorithm to obtain certain strong convergence results. Furthermore, numerical experiments are provided by constructing an example and comparison results have also been incorporated.

scholarly journals Shrinking Projection Methods for Accelerating Relaxed Inertial Tseng-Type Algorithm with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hasanen A. Hammad ◽  
Habib ur Rehman ◽  
Manuel De la Sen
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Minimization Problem ◽  
Numerical Experiments ◽  
Real Hilbert Space ◽  
Projection Methods ◽  
Novel Structure ◽  
Convergence Results ◽  
Type Algorithm ◽  
Shrinking Projection Methods

Our main goal in this manuscript is to accelerate the relaxed inertial Tseng-type (RITT) algorithm by adding a shrinking projection (SP) term to the algorithm. Hence, strong convergence results were obtained in a real Hilbert space (RHS). A novel structure was used to solve an inclusion and a minimization problem under proper hypotheses. Finally, numerical experiments to elucidate the applications, performance, quickness, and effectiveness of our procedure are discussed.

Existence and convergence for a new multivalued hybrid mapping in CAT(κ) spaces

2017 ◽  
Vol 33 (3) ◽  
pp. 319-326
Author(s):  
EMIRHAN HACIOGLU ◽  
◽  
VATAN KARAKAYA ◽  
Keyword(s):  
Hilbert Spaces ◽  
Multivalued Mappings ◽  
Hybrid Mapping ◽  
New Class ◽  
Convergence Results

Most of the studies about hybrid mappings are carried out for single-valued mappings in Hilbert spaces. We define a new class of multivalued mappings in CAT (k) spaces which contains the multivalued generalization of (α, β) - hybrid mappings defined on Hilbert spaces. In this paper, we prove existence and convergence results for a new class of multivalued hybrid mappings on CAT(κ) spaces which are more general than Hilbert spaces and CAT(0) spaces.

scholarly journals On Convergence Results for Lipschitz Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Shin Min Kang ◽  
Arif Rafiq
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iteration Scheme ◽  
Independent Interest ◽  
Ishikawa Iteration ◽  
Pseudocontractive Mappings ◽  
Convergence Results

We establish the strong convergence for the Ishikawa iteration scheme associated with Lipschitz pseudocontractive mappings in real Banach spaces. Moreover, our technique of proofs is of independent interest.

Strong and weak convergence theorems for fixed points of a class of nonlinear mappings

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Changqun Wu ◽  
Zhiqiang Wei ◽  
Yu Li
Keyword(s):  
Weak Convergence ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings ◽  
Weak Convergence Theorem

AbstractIn this paper, the class of total asymptotically nonexpansive mappings is considered. A weak convergence theorem of Mann-type iterative algorithm is established. Hybrid projection methods are considered for the class of total asymptotically nonexpansive mappings. Strong convergence theorems are also established in the framework of Hilbert spaces.

scholarly journals New extragradient methods with non-convex combination for pseudomonotone equilibrium problems with applications in Hilbert spaces

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1677-1693 ◽  
Author(s):  
Shenghua Wang ◽  
Yifan Zhang ◽  
Ping Ping ◽  
Yeol Cho ◽  
Haichao Guo
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Convex Combination ◽  
Projection Methods ◽  
Extragradient Methods ◽  
Numerical Examples

In the literature, the most authors modify the viscosity methods or hybrid projection methods to construct the strong convergence algorithms for solving the pseudomonotone equilibrium problems. In this paper, we introduce some new extragradient methods with non-convex combination to solve the pseudomonotone equilibrium problems in Hilbert space and prove the strong convergence for the constructed algorithms. Our algorithms are very different with the existing ones in the literatures. As the application, the fixed point theorems for strict pseudo-contraction are considered. Finally, some numerical examples are given to show the effectiveness of the algorithms.

Fixed Point Iterations of Asymptotically Demicontractive and Asymptotically Hemicontractive Mappings in Hyperbolic Spaces

2021 ◽  
pp. 2150154
Author(s):  
Hafiz Fukhar-ud-Din ◽  
Safeer Hussain Khan
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Hyperbolic Spaces ◽  
Convergence Results ◽  
Linear And Nonlinear ◽  
Hemicontractive Mappings ◽  
Fixed Point Iterations

In this paper, we obtain strong convergence results for asymptotically demicontractive and asymptotically hemicontractive mappings in hyperbolic spaces. We present our results in hyperbolic spaces. This class of spaces contains both linear and nonlinear spaces like CAT(0) spaces, [Formula: see text]-trees, Banach spaces and Hilbert spaces. Thus our results are not only novel but also much more general.

Sign in / Sign up

Export Citation Format

Share Document