scholarly journals An Iterative Approach to the Solutions of Proximal Split Feasibility Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 145
Author(s):  
Li-Jun Zhu ◽  
Yonghong Yao
Keyword(s):  
Strong Convergence ◽  
Convergence Analysis ◽  
Hilbert Spaces ◽  
Iterative Procedure ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Iterative Approach ◽  
Split Feasibility Problems ◽  
Proximal Split Feasibility Problems ◽  
Split Feasibility

The proximal split feasibility problem is investigated in Hilbert spaces. An iterative procedure is introduced for finding the solution of the proximal split feasibility problem. Strong convergence analysis of the presented algorithm is proved.

scholarly journals Solving a Split Feasibility Problem by the Strong Convergence of Two Projection Algorithms in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hasanen A. Hammad ◽  
Habib ur Rehman ◽  
Yaé Ulrich Gaba
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Convergence Theorems ◽  
Numerical Examples ◽  
Convex Feasibility ◽  
Split Feasibility

The goal of this manuscript is to establish strong convergence theorems for inertial shrinking projection and CQ algorithms to solve a split convex feasibility problem in real Hilbert spaces. Finally, numerical examples were obtained to discuss the performance and effectiveness of our algorithms and compare the proposed algorithms with the previous shrinking projection, hybrid projection, and inertial forward-backward methods.

scholarly journals A general convergence theorem for multiple-set split feasibility problem in Hilbert spaces

2015 ◽  
Vol 31 (3) ◽  
pp. 349-357
Author(s):  
ABDUL RAHIM KHAN ◽  
◽  
MUJAHID ABBAS ◽  
YEKINI SHEHU ◽  
◽  
...  
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Split Feasibility Problem ◽  
Contractive Mapping ◽  
Convergence Result ◽  
Feasibility Problem ◽  
Infinite Dimensional ◽  
Split Feasibility ◽  
General Convergence

We establish strong convergence result of split feasibility problem for a family of quasi-nonexpansive multi-valued mappings and a total asymptotically strict pseudo-contractive mapping in infinite dimensional Hilbert spaces.

scholarly journals General Split Feasibility Problems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammad Eslamian ◽  
Abdul Latif
Keyword(s):  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Infinite Dimensional ◽  
Split Feasibility Problems ◽  
Split Feasibility

Introducing a general split feasibility problem in the setting of infinite-dimensional Hilbert spaces, we prove that the sequence generated by the purposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.

scholarly journals The Split Feasibility Problems for Countable Families of Asymptotically Strict Pseudocontractions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Wei-Qi Deng
Keyword(s):  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Related Research ◽  
Split Feasibility Problems ◽  
The Split Feasibility Problem ◽  
Split Feasibility ◽  
Research Studies

An up-to-date algorithm for solving the split feasibility problem for countable families of asymptotically strict pseudocontractions is introduced in the framework of Hilbert spaces. Our results greatly improve and extend those of other authors whose related research studies are restricted to the situation of at most finitely many such mappings.

Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Chibueze C. Okeke ◽  
Lateef O. Jolaoso ◽  
Yekini Shehu
Keyword(s):  
Strong Convergence ◽  
Prior Knowledge ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Weak And Strong Convergence ◽  
Numerical Examples ◽  
Mild Conditions ◽  
Convergence Results ◽  
Split Feasibility

Abstract In this paper, we propose two inertial accelerated algorithms which do not require prior knowledge of operator norm for solving split feasibility problem with multiple output sets in real Hilbert spaces. We prove weak and strong convergence results for approximating the solution of the considered problem under certain mild conditions. We also give some numerical examples to demonstrate the performance and efficiency of our proposed algorithms over some existing related algorithms in the literature.

scholarly journals An intermixed iteration for constrained convex minimization problem and split feasibility problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Kanyanee Saechou ◽  
Atid Kangtunyakarn
Keyword(s):  
Strong Convergence ◽  
Minimization Problem ◽  
Convergence Theorem ◽  
Split Feasibility Problem ◽  
Convex Minimization ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Convex Minimization Problem ◽  
Constrained Convex Minimization Problem ◽  
Split Feasibility

Abstract In this paper, we first introduce the two-step intermixed iteration for finding the common solution of a constrained convex minimization problem, and also we prove a strong convergence theorem for the intermixed algorithm. By using our main theorem, we prove a strong convergence theorem for the split feasibility problem. Finally, we apply our main theorem for the numerical example.

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