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### A Construction of Monotonically Convergent Sequences from Successive Approximations in Certain Banach Spaces.

Numerische Mathematik

### A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses

Applicationes Mathematicae

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 theorem for Mann fixed point iteration procedure.

Applied Mathematics E-Notes [electronic only]

### A Convergence Theorem for Newton-Like Methods in Banach Spaces.

Numerische Mathematik

### A convergent nonlinear splitting via orthogonal projection

Aplikace matematiky

We study the convergence of the iterations in a Hilbert space $V,{x}_{k+1}=W\left(P\right){x}_{k},W\left(P\right)z=w=T\left(Pw+\left(I-P\right)z\right)$, where $T$ maps $V$ into itself and $P$ is a linear projection operator. The iterations converge to the unique fixed point of $T$, if the operator $W\left(P\right)$ is continuous and the Lipschitz constant $∥\left(I-P\right)W\left(P\right)∥<1$. If an operator $W\left({P}_{1}\right)$ satisfies these assumptions and ${P}_{2}$ is an orthogonal projection such that ${P}_{1}{P}_{2}={P}_{2}{P}_{1}={P}_{1}$, then the operator $W\left({P}_{2}\right)$ is defined and continuous in $V$ and satisfies $∥\left(I-{P}_{2}\right)W\left({P}_{2}\right)∥\le ∥\left(I-{P}_{1}\right)W\left({P}_{1}\right)∥$.

### A double-sequence random iteration process for random fixed points of contractive type random operators.

Lobachevskii Journal of Mathematics

### A fixed point theorem

Commentationes Mathematicae Universitatis Carolinae

### 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.)

Abstract and Applied Analysis

### A general iterative algorithm for generalized mixed equilibrium problems and variational inclusions approach to variational inequalities.

International Journal of Mathematics and Mathematical Sciences

### A general iterative approach to variational inequality problems and optimization problems.

Fixed Point Theory and Applications [electronic only]

### A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.

Fixed Point Theory and Applications [electronic only]

### A general iterative method for solving the variational inequality problem and fixed point problem of an infinite family of nonexpansive mappings in Hilbert spaces.

Fixed Point Theory and Applications [electronic only]

### A general iterative method for variational inequality problems, mixed equilibrium problems, and fixed point problems of strictly pseudocontractive mappings in Hilbert spaces.

Fixed Point Theory and Applications [electronic only]

### A general iterative method of fixed points for mixed equilibrium problems and variational inclusion problems.

Journal of Inequalities and Applications [electronic only]

### A general iterative process for solving a system of variational inclusions in Banach spaces.

Journal of Inequalities and Applications [electronic only]

### A general semilocal convergence result for Newton’s method under centered conditions for the second derivative

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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

ESAIM: Mathematical Modelling and Numerical Analysis

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.

Numerische Mathematik

### A generalization of Edelstein's theorem on fixed points and applications.

Southwest Journal of Pure and Applied Mathematics [electronic only]

### A generalization of the Opial's theorem

Control and Cybernetics

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