Implicit and explicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings.
Implicit approximation methods for common fixed points of a finite family of strictly pseudocontractive mappings in Banach spaces
Implicit iteration methods with errors for discrete non-Lipschitzian families with perturbed mappings.
Implicit iteration process for common fixed points of strictly asymptotically pseudocontractive mappings in Banach spaces.
Implicit iteration process of nonexpansive non-self-mappings.
Improved ball convergence of Newton's method under general conditions
We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of...
Inertial forward-backward splitting method in Banach spaces with application to compressed sensing
We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the few available inertial-type methods for zeros of the sum of accretive operators in Banach spaces.
Inexact Newton method under weak and center-weak Lipschitz conditions
The paper develops semilocal convergence of Inexact Newton Method INM for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The results obtained compare favorably with earlier ones in at least the case of Newton's Method (NM). Numerical examples, where our convergence criteria are satisfied but the earlier ones are not, are also explored.
Inexact Newton methods and recurrent functions
We provide a semilocal convergence analysis for approximating a solution of an equation in a Banach space setting using an inexact Newton method. By using recurrent functions, we provide under the same or weaker hypotheses: finer error bounds on the distances involved, and an at least as precise information on the location of the solution as in earlier papers. Moreover, if the splitting method is used, we show that a smaller number of inner/outer iterations can be obtained. Furthermore, numerical...
Integrable solutions of a functional-integral equation.
This paper contains a theorem on the existence of monotonic and integrable solutions of a functional-integral equation. The proof of that theorem is based on the technique associated with the notion of a measure of weak noncompactness.
Inverting the p-harmonic operator.
Ishikawa iteration process with errors for nonexpansive mappings.
Ishikawa iteration process with errors for nonexpansive mappings in uniformly convex Banach spaces.
Ishikawa iterative process for a pair of single-valued and multivalued nonexpansive mappings in Banach spaces.
Ishikawa iterative process with errors for generalized Lipschitzian and Phi-accretive mappings in uniformly smooth Banach spaces
Ishikawa iterative sequence for the generalized Lipschitzian and Phi-strongly accretive mappings in Banach spaces
Ishikawa iterative sequence with errors for strongly pseudocontractive operators in arbitrary Banach spaces.
Iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings.
Iterations of asymptotically pseudocontractive mappings in Banach spaces.
Iterative algorithm for a convex feasibility problem.