Eigenvalues and ranges for perturbations of nonlinear accretive and monotone operators in Banach spaces.
Ein „merkwürdiges” Spektrum für nichtlineare Operatoren
We define a spectrum for Lipschitz continuous nonlinear operators in Banach spaces by means of a certain kind of "pseudo-adjoint" and study some of its properties.
Einige Anwendungen der mehrdimensionalen approximationstheorie zur Lösungseinschließung bei Randwertaufgaben
Enclosing roots of polynomial equations and their applications to iterative processes.
Enlargement Procedure for Resolution of Singularities at Simple Singular Solutions of Nonlinear Equations.
Equivalence and stability of random fixed point iterative procedures.
Erratum to “Iterative methods for variational inequalities over the intersection of the fixed points set of a nonexpansive semigroup in Banach spaces”.
Error bounds for Newton's method under a weak Kantorovich-type hypothesis.
Error bounds for the secant method
Error Bounds of Newton Type Process on Banach Spaces.
Esquisse d'une théorie décompositionnelle
Existence of solutions and convergence of a multistep iterative algorithm for a system of variational inclusions with -accretive operators.
Existence of zeros for operators taking their values in the dual of a Banach space.
Existence theorems of solutions for a system of nonlinear inclusions with an application.
Expanding the applicability of two-point Newton-like methods under generalized conditions
We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied....
Extending the applicability of Newton's method using nondiscrete induction
We extend the applicability of Newton's method for approximating a solution of a nonlinear operator equation in a Banach space setting using nondiscrete mathematical induction concept introduced by Potra and Pták. We obtain new sufficient convergence conditions for Newton's method using Lipschitz and center-Lipschitz conditions instead of only the Lipschitz condition used in F. A. Potra, V. Pták, Sharp error bounds for Newton's process, Numer. Math., 34 (1980), 63–72, and F. A. Potra, V. Pták, Nondiscrete...
Extensions of some Fixed Point Theorems of Rhoades, Ćirić, Maiti and Pal
External approximation of bifurcation problems