A further necessary and sufficient condition for strong convergence of nonlinear contraction semigroups and of iterative methods for accretive operators in Banach spaces

DOI10.1017/S0013091500006167zbMath0820.47074MaRDI QIDQ4697881

G. F. Roach, Yao-Lin Jiang, Zong Ben Xu

Publication date: 6 September 1995

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

zbMATH Keywords

strong convergencenearest point mappingconvergence conditionnonlinear contraction semigroupdemipositive operatorsemigroup generated by a \(m\)-accretive operator and of the steepest descent approximation process

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Nonlinear accretive operators, dissipative operators, etc. (47H06) Equations involving nonlinear operators (general) (47J05) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

On conditions of weak convergence of nonlinear contraction semigroups and of iterative methods for accretive operators in Banach spaces ⋮ New convergence theorems for certain iterative schemes in Banach spaces ⋮ Unnamed Item ⋮ An algorithm for computing zeros of generalized phi-strongly monotone and bounded maps in classical Banach spaces ⋮ COMPUTATION OF ZEROS OF MONOTONE TYPE MAPPINGS: ON CHIDUME’S OPEN PROBLEM ⋮ A Strong Convergence Theorem for an Iterative Method for Finding Zeros of Maximal Monotone Maps with Applications to Convex Minimization and Variational Inequality Problems

Cites Work

• Unnamed Item
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces
• On the asymptotic behavior of nonlinear semigroups and the range of accretive operators
• Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
• A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations
• Asymptotic convergence of nonlinear contraction semigroups in Hilbert space
• Asymptotic behavior of semigroups on nonlinear contractions in Banach spaces
• On the range of accretive operators
• Asymptotic behavior of nonexpansive mappings
• A general convergence principle in nonlinear functional analysis
• An iterative solution of a variational inequality for certain monotone operators in Hilbert space
• Nonlinear mappings of nonexpansive and accretive type in Banach spaces