A Construction of Monotonically Convergent Sequences from Successive Approximations in Certain Banach Spaces.
A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses
The Newton-Kantorovich approach and the majorant principle are used to provide new local and semilocal convergence results for Newton-like methods using outer or generalized inverses in a Banach space setting. Using the same conditions as before, we provide more precise information on the location of the solution and on the error bounds on the distances involved. Moreover since our Newton-Kantorovich-type hypothesis is weaker than before, we can cover cases where the original Newton-Kantorovich...
A convergence result and numerical study for a nonlinear piezoelectric material in a frictional contact process with a conductive foundation
We consider two static problems which describe the contact between a piezoelectric body and an obstacle, the so-called foundation. The constitutive relation of the material is assumed to be electro-elastic and involves the nonlinear elastic constitutive Hencky's law. In the first problem, the contact is assumed to be frictionless, and the foundation is nonconductive, while in the second it is supposed to be frictional, and the foundation is electrically conductive. The contact is modeled with the...
A convergence theorem for Mann fixed point iteration procedure.
A Convergence Theorem for Newton-Like Methods in Banach Spaces.
A convergent nonlinear splitting via orthogonal projection
We study the convergence of the iterations in a Hilbert space , where maps into itself and is a linear projection operator. The iterations converge to the unique fixed point of , if the operator is continuous and the Lipschitz constant . If an operator satisfies these assumptions and is an orthogonal projection such that , then the operator is defined and continuous in and satisfies .
A double-sequence random iteration process for random fixed points of contractive type random operators.
A fixed point theorem
A general composite algorithm for solving general equilibrium problems and fixed point problems in Hilbert spaces. (A general composite algorithms for solving general equilibrium problems and fixed point problems in Hilbert spaces.)
A general iterative algorithm for generalized mixed equilibrium problems and variational inclusions approach to variational inequalities.
A general iterative approach to variational inequality problems and optimization problems.
A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.
A general iterative method for solving the variational inequality problem and fixed point problem of an infinite family of nonexpansive mappings in Hilbert spaces.
A general iterative method for variational inequality problems, mixed equilibrium problems, and fixed point problems of strictly pseudocontractive mappings in Hilbert spaces.
A general iterative method of fixed points for mixed equilibrium problems and variational inclusion problems.
A general iterative process for solving a system of variational inclusions in Banach spaces.
A general semilocal convergence result for Newton’s method under centered conditions for the second derivative
From Kantorovich’s theory we present a semilocal convergence result for Newton’s method which is based mainly on a modification of the condition required to the second derivative of the operator involved. In particular, instead of requiring that the second derivative is bounded, we demand that it is centered. As a consequence, we obtain a modification of the starting points for Newton’s method. We illustrate this study with applications to nonlinear integral equations of mixed Hammerstein type.
A general semilocal convergence result for Newton’s method under centered conditions for the second derivative
From Kantorovich’s theory we present a semilocal convergence result for Newton’s method which is based mainly on a modification of the condition required to the second derivative of the operator involved. In particular, instead of requiring that the second derivative is bounded, we demand that it is centered. As a consequence, we obtain a modification of the starting points for Newton’s method. We illustrate this study with applications to nonlinear...
A Generalisation of Régula Falsi.
A generalization of Edelstein's theorem on fixed points and applications.