A generalization of the Opial's theorem
A generalized hybrid steepest-descent method for variational inequalities in Banach spaces.
A generalized iterative algorithm for generalized successively pseudocontractions.
A hybrid extragradient viscosity approximation method for solving equilibrium problems and fixed point problems of infinitely many nonexpansive mappings.
A hybrid iterative scheme for a maximal monotone operator and two countable families of relatively quasi-nonexpansive mappings for generalized mixed equilibrium and variational inequality problems.
A hybrid projection algorithm for finding solutions of mixed equilibrium problem and variational inequality problem.
A hybrid-extragradient scheme for system of equilibrium problems, nonexpansive mappings, and monotone mappings.
A la recherche du spectre perdu: An invitation to nonlinear spectral theory
We give a survey on spectra for various classes of nonlinear operators, with a particular emphasis on a comparison of their advantages and drawbacks. Here the most useful spectra are the asymptotic spectrum by M. Furi, M. Martelli and A. Vignoli (1978), the global spectrum by W. Feng (1997), and the local spectrum (called “phantom”) by P. Santucci and M. Väth (2000). In the last part we discuss these spectra for homogeneous operators (of any degree), and derive a discreteness result and a nonlinear...
A local convergence analysis and applications of Newton's method under weak assumptions.
A local convergence theorem for the inexact Newton method at singular points.
A method for a solution of equilibrium problem and fixed point problem of a nonexpansive semigroup in Hilbert's spaces.
A Method for Finding Sharp Error Bounds for Newton's Method Under the Kantorovich Assumptions.
A modification of the Kantorovich conditions for the secant method.
A modified iterative process for common fixed points of two finite families of nonexpansive mappings.
A monotone convergence theorem for Newton-like methods using hypotheses on divided differences of order two.
A new approach for finding weaker conditions for the convergence of Newton's method
The Newton-Kantorovich hypothesis (15) has been used for a long time as a sufficient condition for convergence of Newton's method to a locally unique solution of a nonlinear equation in a Banach space setting. Recently in [3], [4] we showed that this hypothesis can always be replaced by a condition weaker in general (see (18), (19) or (20)) whose verification requires the same computational cost. Moreover, finer error bounds and at least as precise information on the location of the solution can...
A new approximation method for common fixed points of a finite family of generalized asymptotically quasinonexpansive mappings in Banach spaces.
A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings.
A new approximation scheme combining the viscosity method with extragradient method for mixed equilibrium problems.
A new composite implicit iterative process for a finite family of nonexpansive mappings in Banach spaces.