Mixed iterative algorithms for the multiple-set split equality common fixed-point problems without prior knowledge of operator norms

Optimization ◽  
2015 ◽  
Vol 65 (5) ◽  
pp. 1069-1083 ◽  
Author(s):  
Jing Zhao ◽  
Shengnan Wang
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Prior Knowledge ◽  
Iterative Algorithms ◽  
Fixed Point Problems ◽  
Operator Norms

scholarly journals Viscosity Methods and Split Common Fixed Point Problems for Demicontractive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 844 ◽  
Author(s):  
Yaqin Wang ◽  
Xiaoli Fang ◽  
Tae-Hwa Kim
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
A Priori ◽  
Fixed Point Problems ◽  
A Priori Knowledge ◽  
Type Algorithm ◽  
Operator Norms ◽  
Demicontractive Mappings ◽  
Split Common Fixed Point

We, first, propose a new method for solving split common fixed point problems for demicontractive mappings in Hilbert spaces, and then establish the strong convergence of such an algorithm, which extends the Halpern type algorithm studied by Wang and Xu to a viscosity iteration. Above all, the step sizes in this algorithm are chosen without a priori knowledge of the operator norms.

scholarly journals Mixed Simultaneous Iterative Algorithms for the Extended Multiple-Set Split Equality Common Fixed-Point Problem with Lipschitz Quasi-Pseudocontractive Operators

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Meixia Li ◽  
Xueling Zhou ◽  
Haitao Che
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Numerical Results ◽  
Point Problem ◽  
Nonexpansive Operator ◽  
Common Fixed Point Problem ◽  
Operator Norms ◽  
Priori Information

In this paper, we study a kind of extended multiple-set split equality common fixed-point problem with Lipschitz quasi-pseudocontractive operators, which is an extension of multiple-set split equality common fixed-point problem with quasi-nonexpansive operator. We propose two mixed simultaneous iterative algorithms, in which the selecting of the stepsize does not need any priori information about the operator norms. Furthermore, we prove that the sequences generated by the mixed simultaneous iterative algorithms converge weakly to the solution of this problem. Some numerical results are shown to illustrate the feasibility and efficiency of the proposed algorithms.

scholarly journals Two iterative algorithms for solving the split common fixed point problems

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4375-4386
Author(s):  
Dingping Wu ◽  
Mihai Postolache
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithm ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Fixed Point Problems ◽  
Split Common Fixed Point

The purpose of this paper is to study the split common fixed point problems (SCFP) involved in nonexpansive mappings in real Hilbert space. We introduce two iterative algorithms for finding a solution of the SCFP involved in nonexpansive mappings, where one is a Mann-type iterative algorithm and another is a Halpern-type iterative algorithm.

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.

Sign in / Sign up

Export Citation Format

Share Document