Semi-Iterative Methods for the Approximate Solution of Ill-Posed Problems.
Semilinear problems with a non-symmetric linear part having an infinite dimensional kernel.
Semilocal analysis of equations with smooth operators.
Semilocal convergence for Newton's method on a Banach space with a convergence structure and twice Fréchet differentiable operators.
Sets in the ranges of nonlinear accretive operators in Banach spaces
Let X be a real Banach space and G ⊂ X open and bounded. Assume that one of the following conditions is satisfied: (i) X* is uniformly convex and T:Ḡ→ X is demicontinuous and accretive; (ii) T:Ḡ→ X is continuous and accretive; (iii) T:X ⊃ D(T)→ X is m-accretive and Ḡ ⊂ D(T). Assume, further, that M ⊂ X is pathwise connected and such that M ∩ TG ≠ ∅ and . Then . If, moreover, Case (i) or (ii) holds and T is of type , or Case (iii) holds and T is of type , then M ⊂ TG. Various results of Morales,...
Shrinking projection method of common solutions for generalized equilibrium quasi--nonexpansive mapping and relatively nonexpansive mapping.
Small functions and iterative methods
Iterative methods based on small functions are used both to show local surjectivity of certain operators and a fixed point property of mappings on scales of complete metric spaces.
Solution Manifolds and Submanifolds of Parametrized Equations and Their Discretization Errors.
Solutions numériques de problèmes de bifurcation
Solving some nonlinear equations by successive approximations.
Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions
We prove the existence of a sequence satisfying , where f is a function whose second order Fréchet derivative ∇²f satifies a center-Hölder condition and F is a set-valued map from a Banach space X to the subsets of a Banach space Y. We show that the convergence of this method is superquadratic.
Some characterizations for a family of nonexpansive mappings and convergence of a generated sequence to their common fixed point.
Some common fixed point theorems in normed linear spaces
In this paper, we establish some generalizations to approximate common fixed points for selfmappings in a normed linear space using the modified Ishikawa iteration process with errors in the sense of Liu [10] and Rafiq [14]. We use a more general contractive condition than those of Rafiq [14] to establish our results. Our results, therefore, not only improve a multitude of common fixed point results in literature but also generalize some of the results of Berinde [3], Rhoades [15] and recent results...
Some convergence results for fixed points of hemicontractive operators in some Banach spaces
Some convergence results for the Jungck--Mann and the Jungck--Ishikawa iteration processes in the class of generalized Zamfirescu operators.
Some convergence theorems of a sequence in complete metric spaces and its applications.
Some fixed point iteration procedures.
Some iterative methods for solving equilibrium problems and optimization problems.
Some mapping theorems and solvability of nonlinear equations in Banach spaces (Preliminary communication)
Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods
First, a result of J. W. Schmidt about the monotone enclosure of solutions of nonlinear equations is generalized. Then an iteration method is considered, which is more effective than other known methods. For this method, monotone enclosure statements are also proved.