Journal Article10.1007/S11075-020-00937-2
Halpern-type iterative process for solving split common fixed point and monotone variational inclusion problem between Banach spaces
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TL;DR: 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.
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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.
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Citations
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.
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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.
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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.
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Relaxed inertial Tseng extragradient method for variational inequality and fixed point problems
Abstract: In this paper, we introduce a new relaxed inertial Tseng extragradient method with self-adaptive step size for approximating common solutions of monotone variational inequality and fixed point problems of quasi-pseudo-contraction mappings in real Hilbert spaces. We prove a strong convergence result for the proposed algorithm without the knowledge of the Lipschitz constant of the cost operator. Moreover, we apply our results to approximate solution of convex minimization problem, and we present some numerical experiments to show the efficiency and applicability of our method in comparison with some existing methods in the literature. Our proposed method is easy to implement. It requires only one projection onto a constructible half-space.
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Inertial-Type Algorithm for Solving Split Common Fixed Point Problems in Banach Spaces
TL;DR: In this article, an inertial-type shrinking projection algorithm was proposed for solving the two-set split common fixed point problems and proved a strong convergence theorem. But it does not solve the split monotone inclusion problem.
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Yair Censor,Tommy Elfving +1 more
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