Nonlinear symmetric positive systems
Non-monotoneous parallel iteration for solving convex feasibility problems
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in an Euclidean space, sometimes leads to slow convergence of the constructed sequence. Such slow convergence depends both on the choice of the starting point and on the monotoneous behaviour of the usual algorithms. As there is normally no indication of how to choose the starting point in order to avoid slow convergence, we present in this paper a non-monotoneous parallel algorithm...
Nonresonance conditions at the two first eigenvalues for semilinear equations
Note on some results for asymptotically pseudocontractive mappings and asymptotically nonexpansive mappings.
Note on weakly inward mappings
The Nielsen fixed point theory is used to show several results for certain operator equations involving weakly inward mappings.
Numerical Computation of Nonsimple Turning Points and Cusps.
Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities
In this paper, some ideas for the numerical realization of the hybrid proximal projection algorithm from Solodov and Svaiter [22] are presented. An example is given which shows that this hybrid algorithm does not generate a Fejér-monotone sequence. Further, a strategy is suggested for the computation of inexact solutions of the auxiliary problems with a certain tolerance. For that purpose, ε-subdifferentials of the auxiliary functions and the bundle trust region method from Schramm and Zowe [20]...
On a class of iterative procedures for solving nonlinear equations in Banach spaces
On a hybrid method for generalized mixed equilibrium problem and fixed point problem of a family of quasi--asymptotically nonexpansive mappings in Banach spaces.
On a new method for enlarging the radius of convergence for Newton's method
We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the mth-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.
On a nonlinear integral equation with contractive perturbation.
On a quadratically convergent method using divided differences of order one under the gamma condition
We re-examine a quadratically convergent method using divided differences of order one in order to approximate a locally unique solution of an equation in a Banach space setting [4, 5, 7]. Recently in [4, 5, 7], using Lipschitz conditions, and a Newton-Kantorovich type approach, we provided a local as well as a semilocal convergence analysis for this method which compares favorably to other methods using two function evaluations such as the Steffensen’s method [1, 3, 13]. Here, we provide an analysis...
On a secant-like method for solving generalized equations
In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances involved and a larger radius of convergence are obtained.
On a two-step algorithm for hierarchical fixed point problems and variational inequalities.
On accretive multivalued mappings in Banach spaces
On an application of a Newton-like method to the approximation of implicit functions
On common fixed points of asymptotically nonexpansive mappings in the intermediate sense
Some strong convergence theorems of common fixed points of asymptotically nonexpansive mappings in the intermediate sense are obtained. The results presented in this paper improve and extend the corresponding results in Huang, Khan and Takahashi, Chang, Schu, and Rhoades.
On equivalence of some iterations convergence for quasi-contraction maps in convex metric spaces.
On fixed points of pseudocontractive mappings.
On iterative solution of nonlinear functional equations in a metric space.