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 Approximation of Fixed Points for Enriched Suzuki Nonexpansive Operators with an Application in Hilbert Spaces

Axioms ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 14
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Muhammad Arshad ◽  
Zhenhua Ma
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
New Class ◽  
Krasnoselskii Iteration ◽  
Nonexpansive Operators ◽  
Split Feasibility

In this article, we introduce the class of enriched Suzuki nonexpansive (ESN) mappings. We show that this new class of mappings properly contains the class of Suzuki nonexpansive as well as the class of enriched nonexpansive mappings. We establish existence of fixed point and convergence of fixed point in a Hilbert space setting under the Krasnoselskii iteration process. One of the our main results is applied to solve a split feasibility problem (SFP) in this new setting of mappings. Our main results are a significant improvement of the corresponding results of the literature.

scholarly journals Approximation of a Common Element of the Fixed Point Sets of Multivalued Strictly Pseudocontractive-Type Mappings and the Set of Solutions of an Equilibrium Problem in Hilbert Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
F. O. Isiogugu
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Contemporary Literature ◽  
Common Element ◽  
Point Sets ◽  
Fixed Point Set ◽  
Strict Fixed Point ◽  
Point Set ◽  
Fixed Point Sets

The strong convergence of a hybrid algorithm to a common element of the fixed point sets of multivalued strictly pseudocontractive-type mappings and the set of solutions of an equilibrium problem in Hilbert spaces is obtained using a strict fixed point set condition. The obtained results improve, complement, and extend the results on multivalued and single-valued mappings in the contemporary literature.

scholarly journals Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-32 ◽  
Author(s):  
Zhao-Rong Kong ◽  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Split Feasibility Problem ◽  
Common Element ◽  
Feasibility Problem ◽  
Fixed Point Set ◽  
Strictly Pseudocontractive Mapping ◽  
Extragradient Methods ◽  
Infinite Dimensional ◽  
Point Set ◽  
Split Feasibility

We consider and study the modified extragradient methods for finding a common element of the solution setΓof a split feasibility problem (SFP) and the fixed point setFix(S)of a strictly pseudocontractive mappingSin the setting of infinite-dimensional Hilbert spaces. We propose an extragradient algorithm for finding an element ofFix(S)∩ΓwhereSis strictly pseudocontractive. It is proven that the sequences generated by the proposed algorithm converge weakly to an element ofFix(S)∩Γ. We also propose another extragradient-like algorithm for finding an element ofFix(S)∩ΓwhereS:C→Cis nonexpansive. It is shown that the sequences generated by the proposed algorithm converge strongly to an element ofFix(S)∩Γ.

Generalized relaxed inertial method with regularization for solving split feasibility problems in real Hilbert spaces

2021 ◽  
pp. 2250106
Author(s):  
A. A. Mebawondu ◽  
L. O. Jolaoso ◽  
H. A. Abass ◽  
O. K. Narain
Keyword(s):  
Hilbert Spaces ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Split Feasibility Problem ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Point Problem ◽  
Inertial Method ◽  
Split Feasibility

In this paper, we propose a new modified relaxed inertial regularization method for finding a common solution of a generalized split feasibility problem, the zeros of sum of maximal monotone operators, and fixed point problem of two nonlinear mappings in real Hilbert spaces. We prove that the proposed method converges strongly to a minimum-norm solution of the aforementioned problems without using the conventional two cases approach. In addition, we apply our convergence results to the classical variational inequality and equilibrium problems, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other existing methods in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

scholarly journals Shrinking Projection Methods for Split Common Fixed-Point Problems in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Huan-chun Wu ◽  
Cao-zong Cheng
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Split Common Fixed Point

Inspired by Moudafi (2011) and Takahashi et al. (2008), we present the shrinking projection method for the split common fixed-point problem in Hilbert spaces, and we obtain the strong convergence theorem. As a special case, the split feasibility problem is also considered.

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