Strong Convergence of a Proximal-Type Algorithm in a Banach Space
By Shoji Kamimura, Wataru Takahashi. SIAM Journal on Optimization, 2002
761 citations recorded by the source corpus.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/5587744e319b61996f66fc6ae4900d49b290b69e
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In Computational Theory and Mathematics
- Yonghong Yao
- Poom Kumam
- Yongfu Su
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- Naseer Shahzad
- Giuseppe Marino
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In Geometry and Topology
In Numerical Analysis
Citations in the corpus
- A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces (2010, background): “Existence and uniqueness of the operatorΠC follow from the properties of the functional φ(x, y) and strict monotonicity of the mapping J (see, for example [47,46,44,48,45]).”
- Generalized Projection Algorithms for Nonlinear Operators (2007, background): “2 (Kamimura and Takahashi [ 12 ]) ”
- Generalized mixed equilibrium problem in Banach spaces (2009, background): “Lemma 1.2 [ 8 ] Let E be a smooth and uniformly convex Banach space.”
- Fixed Point Theorems and Ergodic Theorems for Nonlinear Mappings in Hilbert Spaces (2011, neutral): “for x, y ∈ E ,w hereJ is the duality mapping of E ;s ee [1 ]a nd [ 20 ].”
- Minimum-norm solution of variational inequality and fixed point problem in banach spaces (2015, background): “[10,11,16,35,36] and the references contained therein).”
- Weak convergence of a projection algorithm for variational inequalities in a Banach space (2008, background): “We know the following function studied in Alber [1], Kamimura and Takahashi [11] and Reich [16]: φ(x, y)= ‖x‖2 − 2〈x,Jy〉 + ‖y‖2 for all x, y ∈ E.”
- Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces (2008, neutral): “In this case, we can define the resolvent Jr of A by Jrx =( J + rA) −1 Jx for all x ∈ E; see, for instance, [17, 18 ].”
- Geometric Structures in Tensor Representations (Final Release) (2013, neutral): “Following [21], we can define a function φ : VD‖·‖D ×VD‖·‖D −→ R by φ(u,v) = ‖u‖(2)D − 2〈u, J(v)〉 + ‖v‖ 2 D, where 〈·, ·〉 denotes the duality pairing and J is the normalised duality mapping.”