Generalized split feasibility problem for multi-valued Bregman quasi-nonexpansive mappings in Banach spaces

2021 ◽  
Vol 161 ◽  
pp. 437-451
Author(s):  
Suliman Al-Homidan ◽  
Bashir Ali ◽  
Yusuf I. Suleiman
Keyword(s):  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Split Feasibility

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 Iterative Methods for Finding Solutions of a Class of Split Feasibility Problems over Fixed Point Sets in Hilbert Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1012
Author(s):  
Suthep Suantai ◽  
Narin Petrot ◽  
Montira Suwannaprapa
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Split Feasibility Problem ◽  
Inverse Image ◽  
Feasibility Problem ◽  
Point Sets ◽  
Fixed Point Set ◽  
Split Feasibility ◽  
Fixed Point Sets

We consider the split feasibility problem in Hilbert spaces when the hard constraint is common solutions of zeros of the sum of monotone operators and fixed point sets of a finite family of nonexpansive mappings, while the soft constraint is the inverse image of a fixed point set of a nonexpansive mapping. We introduce iterative algorithms for the weak and strong convergence theorems of the constructed sequences. Some numerical experiments of the introduced algorithm are also discussed.

scholarly journals Multiple-sets split feasibility problem and split equality fixed point problem for firmly quasi-nonexpansive or nonexpansive mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tongxin Xu ◽  
Luoyi Shi
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Point Problem ◽  
Projection Operators ◽  
Nonexpansive Operators ◽  
Split Feasibility

AbstractIn this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem (MSSFP for short) and the split equality fixed point problem (SEFPP for short) with firmly quasi-nonexpansive operators or nonexpansive operators in real Hilbert spaces. Under mild conditions, we prove strong convergence theorems for the algorithm by using the projection method and the properties of projection operators. The result improves and extends the corresponding ones announced by some others in the earlier and recent literature.

scholarly journals New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem

2021 ◽  
Vol 1 (2) ◽  
pp. 106-132
Author(s):  
Austine Efut Ofem ◽  
Unwana Effiong Udofia ◽  
Donatus Ikechi Igbokwe
Keyword(s):  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Almost Contraction ◽  
Contraction Mappings ◽  
Constrained Convex Minimization Problem ◽  
Split Feasibility

The purpose of this paper is to introduce a new iterative algorithm to approximate the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Also, we show that our proposed iterative algorithm converges weakly and strongly to the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Furthermore, it is proved analytically that our new iterative algorithm converges faster than one of the leading iterative algorithms in the literature for almost contraction mappings. Some numerical examples are also provided and used to show that our new iterative algorithm has better rate of convergence than all of S, Picard-S, Thakur and M iterative algorithms for almost contraction mappings and generalized α-nonexpansive mappings. Again, we show that the proposed iterative algorithm is stable with respect to T and data dependent for almost contraction mappings. Some applications of our main results and new iterative algorithm are considered. The results in this article are improvements, generalizations and extensions of several relevant results existing in the literature.

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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