Fixed Point Theory and Applications · 2014 · 57 citations · 16 references
Natural SciencesMathematicsAlgorithmsDifferential EquationsInitial Value ProblemsIntegral EquationsNonlinear DynamicsNumerical AlgorithmsNumerical ConvergenceNumerical Methods For Differential EquationsFredholm Integral EquationsMidpoint RuleNonexpansive MappingsNonlinear Evolution
Abstract The implicit midpoint rule (IMR) for nonexpansive mappings is established. The IMR generates a sequence by an implicit algorithm. Weak convergence of this algorithm is proved in a Hilbert space. Applications to the periodic solution of a nonlinear time-dependent evolution equation and to a Fredholm integral equation are included. MSC: 47J25, 47N20, 34G20, 65J15.
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