A halpern-type iteration for solving the split feasibility problem and the fixed point problem of Bregman relatively nonexpansive semigroup in Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3211-3227 ◽  
Author(s):  
Prasit Cholamjiak ◽  
Pongsakorn Sunthrayuth
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Nonexpansive Semigroup ◽  
Relatively Nonexpansive ◽  
The Split Feasibility Problem ◽  
Split Feasibility

We study the split feasibility problem (SFP) involving the fixed point problems (FPP) in the framework of p-uniformly convex and uniformly smooth Banach spaces. We propose a Halpern-type iterative scheme for solving the solution of SFP and FPP of Bregman relatively nonexpansive semigroup. Then we prove its strong convergence theorem of the sequences generated by our iterative scheme under implemented conditions. We finally provide some numerical examples and demonstrate the efficiency of the proposed algorithm. The obtained result of this paper complements many recent results in this direction.

An iterative algorithm with inertial technique for solving the split common null point problem in Banach spaces

2021 ◽  
pp. 2250120
Author(s):  
Yan Tang ◽  
Pongsakorn Sunthrayuth
Keyword(s):  
Banach Spaces ◽  
Split Feasibility Problem ◽  
Null Point ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Inertial Algorithm ◽  
The Split Feasibility Problem ◽  
Inertial Technique ◽  
Split Feasibility

In this work, we introduce a modified inertial algorithm for solving the split common null point problem without the prior knowledge of the operator norms in Banach spaces. The strong convergence theorem of our method is proved under suitable assumptions. We apply our result to the split feasibility problem, split equilibrium problem and split minimization problem. Finally, we provide some numerical experiments including compressed sensing to illustrate the performances of the proposed method. The result presented in this paper improves and generalizes many recent important results in the literature.

scholarly journals A Modified Halpern's Iterative Scheme for Solving Split Feasibility Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Jitsupa Deepho ◽  
Poom Kumam
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
The Split Feasibility Problem ◽  
Split Feasibility

The purpose of this paper is to introduce and study a modified Halpern’s iterative scheme for solving the split feasibility problem (SFP) in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions a strong convergence theorem is established. The main result presented in this paper improves and extends some recent results done by Xu (Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Problem 26 (2010) 105018) and some others.

scholarly journals Latent Infectious Capacities of Dengue Fever: Mathematical Modeling and Eco-Friendly Prevention Strategy

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 263
Author(s):  
Chung-Chien Hong ◽  
Wei-Shih Du ◽  
Yu-Hong Ge
Keyword(s):  
Mathematical Modeling ◽  
Dengue Fever ◽  
Iterative Scheme ◽  
High Capacity ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Public Data ◽  
The Split Feasibility Problem ◽  
Split Feasibility ◽  
Kaohsiung City

The main aim of this article is to propose a method for exploring the latent values about the capacities of spreading dengue for each potential site. First, a mathematical model connecting the observable public data and the capacities of spreading dengue is provided based on the split feasibility problem (SFP). Then, a proper iterative scheme for the SFP is presented to approach the values of infectious capacities (ICs) of potential sites—the capacities of spreading. The performance of our proposed method is demonstrated using public data from Kaohsiung City for 2014 and 2015. The results presented in this paper show that our proposed method is reliable and the sites with a high capacity of spreading are only a small portion of thousands of all potential sites and could be an alternative strategy for preventing the outbreak of dengue fever whilst also avoiding the damage of ecosystems caused by chemical insecticides.

scholarly journals Convergence Theorem of Two Sequences for Solving the Modified Generalized System of Variational Inequalities and Numerical Analysis

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 916
Author(s):  
Anchalee Sripattanet ◽  
Atid Kangtunyakarn
Keyword(s):  
Variational Inequalities ◽  
Convergence Theorem ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
System Of Variational Inequalities ◽  
Generalized System ◽  
Constrained Convex Minimization Problem ◽  
The Split Feasibility Problem ◽  
Split Feasibility

The purpose of this paper is to introduce an iterative algorithm of two sequences which depend on each other by using the intermixed method. Then, we prove a strong convergence theorem for solving fixed-point problems of nonlinear mappings and we treat two variational inequality problems which form an approximate modified generalized system of variational inequalities (MGSV). By using our main theorem, we obtain the additional results involving the split feasibility problem and the constrained convex minimization problem. In support of our main result, a numerical example is also presented.

scholarly journals Strong Convergence Theorems for Generalized Split Feasibility Problems in Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 892
Author(s):  
Xuejiao Zi ◽  
Zhaoli Ma ◽  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Split Feasibility Problem ◽  
Fixed Point Problems ◽  
Feasibility Problem ◽  
Convergence Theorems ◽  
Split Common Fixed Point ◽  
Split Feasibility

In this paper, we establish new strong convergence theorems of proposed algorithms under suitable new conditions for the generalized split feasibility problem in Banach spaces. As applications, new strong convergence theorems for equilibrium problems, fixed point problems and split common fixed point problems are also studied. Our new results are distinct from recent results on the topic in the literature.

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