Newton-like methods for the computation of fixed points

Newton-like Methods with At least Quadratic Order of Convergence for the Computation of Fixed Points

The well known contraction mapping principle or Banach’s fixed point theorem asserts: The method for successive substitutions converges only linearly to a fixed point of an operator equation in a Banach space setting [5], [7]. In practice, if Newton’s method is used one ignores the additional information about the contraction mapping information. Werner in [9] provided a local analysis for a Ne...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

On the Computation of Nonhyperbolic Fixed Points

Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

A Survey of Categorical Computation: Fixed Points, . . .

E. Moggi, Categories of Partial Morphism and the p -calculus, In Category Theory and Computer Programming, Lecture Notes in Computer Science 240, SpringerVerlag, 1986. [Mog88a] E. Moggi, Computational Lambda-Calculus and Monads, Technical Report ECSLFCS-88-66, University of Edinburgh, October, 1988. [Mog88b] E. Moggi, Partial Morphisms in Categories of E ective Objects, Information and Computat...