scholarly journals A New Iterative Construction for Approximating Solutions of a Split Common Fixed Point Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Huimin He ◽  
Qinwei Fan ◽  
Rudong Chen
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
The Novel ◽  
Vector Sequence ◽  
Analysis Techniques ◽  
Convergence Results ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

In this paper, we aim to construct a new strong convergence algorithm for a split common fixed point problem involving the demicontractive operators. It is proved that the vector sequence generated via the Halpern-like algorithm converges to a solution of the split common fixed point problem in norm. The main convergence results presented in this paper extend and improve some corresponding results announced recently. The highlights of this paper shed on the novel algorithm and the new analysis techniques.

scholarly journals Weak and Strong Convergence of an Algorithm for the Split Common Fixed-Point of Asymptotically Quasi-Nonexpansive Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazheng Dang ◽  
Yan Gao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Weak And Strong Convergence ◽  
Convergence Results ◽  
Common Fixed Point Problem ◽  
Nonexpansive Operators ◽  
Split Common Fixed Point

Inspired by the Moudafi (2010), we propose an algorithm for solving the split common fixed-point problem for a wide class of asymptotically quasi-nonexpansive operators and the weak and strong convergence of the algorithm are shown under some suitable conditions in Hilbert spaces. The algorithm and its convergence results improve and develop previous results for split feasibility problems.

scholarly journals A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 372
Author(s):  
Nishu Gupta ◽  
Mihai Postolache ◽  
Ashish Nandal ◽  
Renu Chugh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Prior Knowledge ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Null Point ◽  
Operator Norm ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

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