A general iterative method for split common fixed point problem and variational inclusion problem

2018 ◽  
Vol 35 (2) ◽  
pp. 591-612 ◽  
Author(s):  
Mohammad Eslamian
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Inclusion Problem ◽  
Point Problem ◽  
Variational Inclusion Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point ◽  
General Iterative Method

scholarly journals The split common fixed point problem of two infinite families of demicontractive mappings and the split common null point problem

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3859-3874 ◽  
Author(s):  
Ali Abkar ◽  
Elahe Shahrosvand
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Null Point ◽  
Inclusion Problem ◽  
Point Problem ◽  
Variational Inclusion Problem ◽  
Common Fixed Point Problem ◽  
Demicontractive Mappings ◽  
Split Common Fixed Point

In this paper we introduce a new algorithm based on the viscosity iteration method for solving the split common fixed point problem of two infinite families of k-demicontractive mappings. We shall also study the split common null point problem, and the split equilibrium problem for this class of mappings. As an application, we obtain strong convergence theorems for the split monotone variational inclusion problem and the split variational inequality problem. Our results improve and extend the recent results of Cui and Wang [9], Takahashi [21], Tang and Lui [22], Moudafi [15], Eslamian and Vahidi [17], and many others.

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.

Generalized self-adaptive algorithm for solving split common fixed point problem and its application to image restoration problem

2019 ◽  
Vol 97 (7) ◽  
pp. 1431-1443 ◽  
Author(s):  
Raweerote Suparatulatorn ◽  
Anchalee Khemphet ◽  
Phakdi Charoensawan ◽  
Suthep Suantai ◽  
Narawadee Phudolsitthiphat
Keyword(s):  
Fixed Point ◽  
Image Restoration ◽  
Common Fixed Point ◽  
Adaptive Algorithm ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point ◽  
Restoration Problem ◽  
Self Adaptive
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