Implicit predictor-corrector iteration process for finitely many asymptotically (quasi-)nonexpansive mappings.
Improved ball convergence of Newton's method under general conditions
We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of...
Inexact Newton method under weak and center-weak Lipschitz conditions
The paper develops semilocal convergence of Inexact Newton Method INM for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The results obtained compare favorably with earlier ones in at least the case of Newton's Method (NM). Numerical examples, where our convergence criteria are satisfied but the earlier ones are not, are also explored.
Inexact Newton methods and recurrent functions
We provide a semilocal convergence analysis for approximating a solution of an equation in a Banach space setting using an inexact Newton method. By using recurrent functions, we provide under the same or weaker hypotheses: finer error bounds on the distances involved, and an at least as precise information on the location of the solution as in earlier papers. Moreover, if the splitting method is used, we show that a smaller number of inner/outer iterations can be obtained. Furthermore, numerical...
Inflated mappings for singularities of codimension
Iterations converging to distinct solutions of some nonlinear operator equations in Banach space.
Iterative algorithms with seminorm-induced oblique projections.
Iterative algorithms with variable coefficients for multivalued generalized -hemicontractive mappings without generalized Lipschitz assumption.
Iterative Einschliessungen von Lösungen nichtlinearer Differentialgleichungen durch Newton-ähnliche Iterationsverfahren
In der vorliegenden Arbeit untersuchen wir monoton einschliessende Newton-ähnliche Iterationsverfahren zur näherungsweisen Lösung verschiedener Klassen vonnichtlinearen Differentialgleichungen. Die behandelten Methoden sind auch für nichtkonvexe Nichtlinearitäten anwendbar. Ferner konstruieren wir einschliessende Startnäherungen für diese Verfahren, so dass wir die Existenz der Lösungen der gegebenen Differentialgleichungen sichern können. Die Konvergenz der Verfahren wird auch für den Fall bewiesen,...
Iterative Lösung gewisser Randwertprobleme und Integralgleichungen
Iterative methods for finding common solution of generalized equilibrium problems and variational inequality problems and fixed point problems of a finite family of nonexpansive mappings.
Iterative methods for -strict pseudo-contractive mappings in Hilbert spaces.
Iterative methods for variational inequalities over the intersection of the fixed points set of a nonexpansive semigroup in Banach spaces.
Iterative schemes for fixed points of relatively nonexpansive mappings and their applications.