Strong and Weak Convergence of the Modified Proximal Point Algorithms in Hilbert Space

Strong and Weak Convergence of the Modified Proximal Point Algorithms in Hilbert Space

Throughout this paper, let H be a real Hilbert space with inner product 〈·, ·〉 and norm ‖ · ‖, and let I be on identity operator inH. We shall denote by N the set of all positive integers, by Z the set of all zeros of T , that is, Z T−10 {x ∈ D T ; 0 ∈ Tx} and by F T the set of all fixed points of T , that is, F T {x ∈ E; Tx x}. When {xn} is a sequence in E, then xn → x resp., xn ⇀ x, xn ∗ ⇀ x ...

Forcing strong convergence of proximal point iterations in a Hilbert space

This paper concerns with convergence properties of the classical proximal point algorithm for finding zeroes of maximal monotone operators in an infinite-dimensional Hilbert space. It is well known that the proximal point algorithm converges weakly to a solution under very mild assumptions. However, it was shown by Güler [11] that the iterates may fail to converge strongly in the infinite-dimen...

Mathematical Programming Manuscript No. Forcing Strong Convergence of Proximal Point Iterations in a Hilbert Space

This paper concerns with convergence properties of the classical proximal point algorithm for nding zeroes of maximal monotone operators in an innnite-dimensional Hilbert space. It is well known that the proximal point algorithm converges weakly to a solution under very mild assumptions. However, it was shown by G uler 11] that the iterates may fail to converge strongly in the innnite-dimension...

Weak and Strong Convergence Theorems for Equilibrium Problems and Countable Strict Pseudocontractions Mappings in Hilbert Space

the investigation of research articles in applied linguistics: convergence and divergence in iranian elt context

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