scholarly journals An iterative algorithm for fixed point problem and convex minimization problem with applications

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Gang Cai ◽  
Yekini Shehu
Keyword(s):  
Fixed Point ◽  
Iterative Algorithm ◽  
Minimization Problem ◽  
Fixed Point Problem ◽  
Convex Minimization ◽  
Point Problem ◽  
Convex Minimization Problem

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.

scholarly journals A Common Solution of Equilibrium, Constrained Convex Minimization, and Fixed Point Problems

2021 ◽  
Vol 52 ◽  
Author(s):  
Maryam Yazdi
Keyword(s):  
Fixed Point ◽  
Iterative Scheme ◽  
Fixed Point Problem ◽  
Convex Minimization ◽  
Projection Algorithm ◽  
Point Problem ◽  
Constrained Convex Minimization ◽  
Common Solution ◽  
Numerical Result ◽  
Constrained Convex Minimization Problem

In this paper, we propose a new iterative scheme with the help of the gradient- projection algorithm (GPA) for finding a common solution of an equilibrium problem, a constrained convex minimization problem, and a fixed point problem. Then, we prove some strong convergence theorems which improve and extend some recent results. Moreover, we give a numerical result to show the validity of our main theorem.

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