A Method for Finding Sharp Error Bounds for Newton's Method Under the Kantorovich Assumptions.
A minimax inequality for a class of functionals and applications to the existence of solutions for two-point boundary-value problems.
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.
-monotonicity and applications to nonlinear variational inclusion problems.
A Morse lemma at infinity for Yamabe type problems on domains
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.
A new convergence theorem for Steffensen's method on Banach spaces and applications.
A new general iterative method for a finite family of nonexpansive mappings in Hilbert spaces.
A new hybrid algorithm for a system of mixed equilibrium problems, fixed point problems for nonexpansive semigroup, and variational inclusion problem.
A new hybrid algorithm for variational inclusions, generalized equilibrium problems, and a finite family of quasi-nonexpansive mappings.
A new hybrid iterative algorithm for fixed-point problems, variational inequality problems, and mixed equilibrium problems.
A new iteration method for nonexpansive mappings and monotone mappings in Hilbert spaces.
A new iteration process for approximation of common fixed points for finite families of total asymptotically nonexpansive mappings.
A new iterative algorithm for approximating common fixed points for asymptotically nonexpansive mappings.