scholarly journals Strong Convergence Theorems by Shrinking Projection Methods for Class T Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Qiao-Li Dong ◽  
Songnian He ◽  
Fang Su
Keyword(s):  
Strong Convergence ◽  
Projection Methods ◽  
Convergence Theorems ◽  
Shrinking Projection Methods

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.

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

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