Journal ArticleDOI
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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Strong convergence theorems for finite families of pseudomonotone equilibrium and fixed point problems in Banach spaces
TL;DR: In this article, a new linesearch technique with Halpern iteration was introduced for finding a common solution of finite families of pseudomonotone equilibrium problems and fixed point of finite family of quasi-consuming mappings in Banach spaces.
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Relaxed inertial Tseng extragradient method for variational inequality and fixed point problems
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Convergence of Relaxed Inertial Subgradient Extragradient Methods for Quasimonotone Variational Inequality Problems
TL;DR: In this article, the authors presented two new relaxed inertial subgradient extragradient methods for solving variational inequality problems in a real Hilbert space, and established the convergence of the sequence generated by these methods when the cost operator is quasimonotone and Lipschitz continuous.
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A modified extragradient algorithm for a certain class of split pseudo-monotone variational inequality problem
TL;DR: In this paper, a modified extragradient algorithm for split pseudo-monotone variational inequality problem in real Hilbert spaces is presented. But the authors do not consider the Lipschitz constant of the pseudo monotone operator.
References
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Signal recovery by proximal forward-backward splitting ∗
TL;DR: It is shown that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties, which makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems.
Book
Topics in metric fixed point theory
Kazimierz Goebel,William A. Kirk +1 more
TL;DR: In this paper, the basic fixed point theorems for non-pansive mappings are discussed and weak sequential approximations are proposed for linear mappings with normal structure and smoothness.
Journal ArticleDOI
A multiprojection algorithm using Bregman projections in a product space
Yair Censor,Tommy Elfving +1 more
TL;DR: Using an extension of Pierra's product space formalism, it is shown here that a multiprojection algorithm converges and is fully simultaneous, i.e., it uses in each iterative stepall sets of the convex feasibility problem.
Journal ArticleDOI
On the maximality of sums of nonlinear monotone operators
TL;DR: In this article, it was shown that for any two monotone operators Tx and T2 from X to X*, the operator F», + T2 is again monotonous.