Journal ArticleDOI
A strong convergence algorithm for a fixed point constrained split null point problem
Olawale Kazeem Oyewole,Olawale Kazeem Oyewole,H. A. Abass,H. A. Abass,Oluwatosin Temitope Mewomo +4 more
- Vol. 70, Iss: 1, pp 389-408
TLDR
In this article, a self-adaptive step-size method for finding a common solution of a split feasibility problem and a fixed point problem in real Hilbert spaces is proposed. But the authors do not consider the operator norm in the proposed method.Abstract:
In this paper, we introduce a new algorithm with self adaptive step-size for finding a common solution of a split feasibility problem and a fixed point problem in real Hilbert spaces. Motivated by the self adaptive step-size method, we incorporate the self adaptive step-size to overcome the difficulty of having to compute the operator norm in the proposed method. Under standard and mild assumption on the control sequences, we establish the strong convergence of the algorithm, obtain a common element in the solution set of a split feasibility problem for sum of two monotone operators and fixed point problem of a demimetric mapping. Numerical examples are presented to illustrate the performance and the behavior of our method. Our result extends, improves and unifies other results in the literature.read more
Citations
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Journal ArticleDOI
An inertial method for solving generalized split feasibility problems over the solution set of monotone variational inclusions
TL;DR: In this paper, an inertial extrapolation method for solving generalized split feasibility problems over the solution set of monotone variational inclusion problems in real Hilbert space is proposed. But this method is not suitable for real Hilbert spaces.
Journal ArticleDOI
An iterative algorithm for solving variational inequality, generalized mixed equilibrium, convex minimization and zeros problems for a class of nonexpansive-type mappings
TL;DR: In this paper, an iterative scheme which combines the inertial subgradient extragradient method with viscosity technique and with self-adaptive stepsize was proposed.
Journal ArticleDOI
Viscosity S-iteration method with inertial technique and self-adaptive step size for split variational inclusion, equilibrium and fixed point problems
Journal ArticleDOI
A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings
Abd-semii Oluwatosin-Enitan Owolabi,Timilehin Opeyemi Alakoya,Adeolu Taiwo,Oluwatosin Temitope Mewomo +3 more
TL;DR: In this article, a modified self-adaptive inertial subgradient extragradient algorithm is presented, in which the two projections are made onto some half spaces and under mild conditions, the sequence generated by the proposed algorithm for approximating a common solution of variational inequality problem and common fixed point of a finite family of demicontractive mappings in a real Hilbert space.
Journal ArticleDOI
Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems
TL;DR: Two new inertial-type algorithms for solving variational inequality problems (VIPs) with monotone and Lipschitz continuous mappings in real Hilbert spaces with strong convergence results are introduced.
References
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Journal ArticleDOI
Averaged Mappings and the Gradient-Projection Algorithm
Hong-Kun Xu,Hong-Kun Xu +1 more
TL;DR: This article provides an alternative averaged mapping approach to the GPA, and provides two modifications of GPA so that strong convergence is guaranteed in infinite-dimensional Hilbert spaces.
Journal ArticleDOI
Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces
Olavi Nevanlinna,Simeon Reich +1 more
TL;DR: In this article, the authors studied a general condition on anm-accretive operators in a Banach space that guarantees strong convergence of the semigroup generated by A and related implicit and explicit iterative schemes to a zero.
Journal ArticleDOI
Approximating Curve and Strong Convergence of the CQ Algorithm for the Split Feasibility Problem
Fenghui Wang,Hong-kun Xu +1 more
TL;DR: In this article, a modification of Byrne's CQ algorithm was introduced in such a way that strong convergence is guaranteed and the limit is also the minimum-norm solution of SFP.
Journal ArticleDOI
Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces
TL;DR: In this paper, generalized split feasibility problems governed by generalized hybrid mappings are studied via iterative methods, and several algorithms are introduced to solve them; weak convergence of these algorithms is proved.
Journal ArticleDOI
The shrinking projection method for a finite family of demimetric mappings with variational inequality problems in a Hilbert space
TL;DR: In this article, a new nonlinear mapping called demimetric and the shrinking projection method are used to find a common element of the set of common fixed points for a finite family of these new mappings in a Hilbert space.