Strong convergence of an iterative sequence for maximal monotone operators in a Banach space

By Fumiaki Kohsaka, Wataru Takahashi. 2004

159 citations recorded by the source corpus.

We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ce2bb40e689c71f831cf662b0f4dd8653062101c

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Weak and Strong Convergence Theorems for Maximal Monotone Operators in a Banach Space (2004, background): “Motivated by Censor and Reich [4], Kohsaka and Takahashi [ 12 ] also introduced the following iterative sequence for a maximal monotone operator T ⊂ E × E ∗ : x1 = x ∈ E and”
Fixed Point Theorems and Ergodic Theorems for Nonlinear Mappings in Hilbert Spaces (2011, unknown): “See [2, 21, 23 , 33, 38] for examples and convergence theorems for nonspreading mappings in a Banach space.”