A Strong Convergence Theorem for an Iterative Method for Finding Zeros of Maximal Monotone Maps with Applications to Convex Minimization and Variational Inequality Problems

DOI10.1017/S0013091518000366OpenAlexW2893094212MaRDI QIDQ5228213

M. I. Uzochukwu, Emmanuel Ezzaka Otubo, Kennedy O. Idu, M. O. Uba, Charles E. Chidume

Publication date: 9 August 2019

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0013091518000366

zbMATH Keywords

strong convergencemonotone mappingmaximal monotone mappings

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Monotone operators and generalizations (47H05) Equations involving nonlinear operators (general) (47J05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Perturbations of nonlinear operators (47H14)

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Cites Work

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• An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems
• A regularization method for the proximal point algorithm
• Iterative approximation of fixed points
• The iterative solution of the equation \(f\in x+Tx\) for a monotone operator T in \(L^ p\) spaces
• Monotone (nonlinear) operators in Hilbert space
• Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Extension problems for accretive sets in Banach spaces
• Projection and proximal point methods: Convergence results and counterexamples.
• A strongly convergent iterative solution of \(0 \in U(x)\) for a maximal monotone operator U in Hilbert space
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Iterative algorithm for zeros of multivalued accretive operators in certain Banach spaces
• Geometric properties of Banach spaces and nonlinear iterations
• Nonlinear semigroups and evolution equations
• A Proximal Point Method for the Variational Inequality Problem in Banach Spaces
• EQUILIBRIUM POINTS FOR A SYSTEM INVOLVING M-ACCRETIVE OPERATORS
• On the projection methods for fixed point problems
• On convergence of the proximal point algorithm in Banach spaces
• Iterative Algorithms for Nonlinear Operators
• Strong convergence theorems for bounded accretive operators in uniformly smooth Banach spaces
• Nonlinear Ill-posed Problems of Monotone Type
• A Hybrid Proximal-Extragradient Algorithm with Inertial Effects
• Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• Approximating Zeros of Accretive Operators
• Monotone Operators and the Proximal Point Algorithm
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• A further necessary and sufficient condition for strong convergence of nonlinear contraction semigroups and of iterative methods for accretive operators in Banach spaces
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• Proximité et dualité dans un espace hilbertien
• Nonlinear mappings of nonexpansive and accretive type in Banach spaces
• Combining The Proximal Algorithm And Tikhonov Regularization

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