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Halpern-type iterative process for solving split common fixed point and monotone variational inclusion problem between Banach spaces
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A Halpern-type algorithm with two self-adaptive stepsizes for obtaining solution of the split common fixed point and monotone variational inclusion problem in uniformly convex and 2-uniformly smooth Banach spaces is proposed and strong convergence theorem for the algorithm is proved.Abstract:
In this paper, we study the split common fixed point and monotone variational inclusion problem in uniformly convex and 2-uniformly smooth Banach spaces. We propose a Halpern-type algorithm with two self-adaptive stepsizes for obtaining solution of the problem and prove strong convergence theorem for the algorithm. Many existing results in literature are derived as corollary to our main result. In addition, we apply our main result to split common minimization problem and fixed point problem and illustrate the efficiency and performance of our algorithm with a numerical example. The main result in this paper extends and generalizes many recent related results in the literature in this direction.read more
Citations
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Inertial methods for finding minimum-norm solutions of the split variational inequality problem beyond monotonicity
TL;DR: This paper presents two new methods with inertial steps for solving the split variational inequality problems in real Hilbert spaces without any product space formulation and proves that the sequence generated by these methods converges strongly to a minimum-norm solution of the problem when the operators are pseudomonotone and Lipschitz continuous.
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
Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
Journal ArticleDOI
Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems
TL;DR: In this paper, Tseng's extragradient algorithm with self-adaptive step size was proposed to solve the variational inequality problem (VIP) and the fixed point problem.
References
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Journal ArticleDOI
Iterative oblique projection onto convex sets and the split feasibility problem
TL;DR: In this article, the authors proposed a block-iterative version of the split feasibility problem (SFP) called the CQ algorithm, which involves only the orthogonal projections onto C and Q, which we shall assume are easily calculated, and involves no matrix inverses.
Posted Content
Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
TL;DR: In this article, a generalized metric projection operator in Banach space is introduced, which is a natural generalization of metric projection operators in Hilbert space and can be used for solving variational inequalities and direct projection equations.
Journal ArticleDOI
Strong Convergence of a Proximal-Type Algorithm in a Banach Space
Shoji Kamimura,Wataru Takahashi +1 more
TL;DR: The purpose is to extend Solodov and Svaiter's result to more general Banach spaces and consider the problem of finding a minimizer of a convex function.