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.
On mesh independence and Newton-type methods
Mesh-independent convergence of Newton-type methods for the solution of nonlinear partial differential equations is discussed. First, under certain local smoothness assumptions, it is shown that by properly relating the mesh parameters and for a coarse and a fine discretization mesh, it suffices to compute the solution of the nonlinear equation on the coarse mesh and subsequently correct it once using the linearized (Newton) equation on the fine mesh. In this way the iteration error will be...
On multipoint iterative processes of efficiency index higher than Newton's method.
On multivalued nonlinear variational inclusion problems with -accretive mappings in Banach spaces.
On Newton-Like Methods.
On stability and growth of solutions for classes of initial and boundary value problems
On strong convergence by the hybrid method for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings.
On -stability of Picard iteration in cone metric spaces.