The implicit midpoint rule for nonexpansive mappings

DOI10.1186/1687-1812-2014-96zbMath1332.47037OpenAlexW2008145369WikidataQ59322594 ScholiaQ59322594MaRDI QIDQ2264175

Maryam A. Alghamdi, Mohammad Ali Alghamdi, Naseer Shahzad, Hong-Kun Xu

Publication date: 20 March 2015

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1812-2014-96

zbMATH Keywords

Fredholm integral equationnonexpansive mappingHilbert spaceperiodic solutionnonlinear evolution equationimplicit midpoint rule

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear differential equations in abstract spaces (34G20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Applications of operator theory to differential and integral equations (47N20) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Splitting-midpoint method for zeros of the sum of accretive operator and \(\mu\)-inversely strongly accretive operator in a \(q\)-uniformly smooth Banach space and its applications ⋮ Ergodicity of the implicit midpoint rule for nonexpansive mappings ⋮ A new iterative algorithm for the sum of infinite \(m\)-accretive mappings and infinite \(\mu_{i}\)-inversely strongly accretive mappings and its applications to integro-differential systems ⋮ The generalized viscosity explicit rules for a family of strictly pseudo-contractive mappings in a \(q\)-uniformly smooth Banach space ⋮ Modified semi-implicit midpoint rule for nonexpansive mappings ⋮ General semi-implicit approximations with errors for common fixed points of nonexpansive-type operators and applications to Stampacchia variational inequality ⋮ A Generalized Nonlinear Iterative Algorithm for the Explicit Midpoint Rule of Nonexpansive Semigroup ⋮ General viscosity implicit midpoint rule for nonexpansive mapping ⋮ Modified forward-backward splitting midpoint method with superposition perturbations for the sum of two kinds of infinite accretive mappings and its applications ⋮ Unnamed Item ⋮ Modified viscosity implicit rules for nonexpansive mappings in Hilbert spaces ⋮ On new Picard-Mann iterative approximations with mixed errors for implicit midpoint rule and applications ⋮ A modified viscosity iterative method for implicit midpoint rule for optimization and fixed point problems in CAT(0) spaces ⋮ Solutions of nonlinear operator equations by viscosity iterative methods ⋮ Viscosity approximation methods for the implicit midpoint rule of asymptotically nonexpansive mapping in complete CAT(0) spaces ⋮ A transformation algorithm for nonexpansive mappings ⋮ More general viscosity implicit midpoint rule for nonexpansive mapping with applications ⋮ The viscosity approximation forward-backward splitting method for the implicit midpoint rule of quasi inclusion problems in Banach spaces ⋮ Viscosity approximation methods for the implicit midpoint rule of nonexpansive mappings in CAT(0) Spaces ⋮ Semi-implicit iterative schemes with perturbed operators for infinite accretive mappings and infinite nonexpansive mappings and their applications to parabolic systems ⋮ Strong Convergence Theorems for the Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in the Intermediate Sense in Hilbert Spaces ⋮ Viscosity implicit iterative algorithms based on generalized contractions for strictly pseudo-contractive mappings in Banach spaces ⋮ Iterative algorithm for a common fixed point of two mono-pseudocontractive mappings in Banach spaces ⋮ New ergodic convergence theorems for non-expansive mappings and \(m\)-accretive mappings ⋮ Convergence analysis of modified viscosity implicit rules of asymptotically nonexpansive mappings in Hilbert spaces ⋮ Unnamed Item ⋮ The implicit midpoint rule of nonexpansive mappings and applications in uniformly smooth Banach spaces ⋮ General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete \(\operatorname{CAT}(0)\) spaces ⋮ The viscosity method for the implicit double midpoint rule with numerical results and its applications ⋮ The implicit midpoint procedures for asymptotically nonexpansive mappings ⋮ The implicit midpoint rule for nonexpansive mappings in 2-uniformly convex hyperbolic spaces ⋮ The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces ⋮ The generalized viscosity explicit rules for solving variational inclusion problems in Banach spaces ⋮ Viscosity explicit midpoint methods for nonexpansive mappings in Hadamard spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perturbation techniques for nonexpansive mappings with applications
• A semi-implicit mid-point rule for stiff systems of ordinary differential equations
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Approximation of fixed points of nonexpansive mappings
• Analysis of the linearly implicit mid-point rule for differential- algebraic equations
• Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case
• Iterative methods for strict pseudo-contractions in Hilbert spaces
• AN IMPLICIT ITERATION PROCESS FOR NONEXPANSIVE MAPPINGS
• Iterative Algorithms for Nonlinear Operators
• Recent Progress in Extrapolation Methods for Ordinary Differential Equations
• Implicit midpoint rule and extrapolation to singularly perturbed boundary alue problems
• Implicit Midpoint Rule to the Nonlinear Degenerate Boundary Value Problems
• Solvability of nonlinear Volterra and Fredholm equations in weighted spaces
• EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR EQUATIONS OF EVOLUTION
• Fixed points of nonexpanding maps
• Mean Value Methods in Iteration