Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications

A unified local convergence for Chebyshev-Halley-type methods in Banach space under weak conditions

We present a unified local convergence analysis for Chebyshev-Halleytype methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Chebyshev; Halley; super-Halley and other high order methods. The convergence ball and error estimates are given for these methods under the same conditions. Numerical examples are also provided in this stu...

The covariation for Banach space valued processes and applications

This article focuses on a recent concept of covariation for processes taking values in a separable Banach space B and a corresponding quadratic variation. The latter is more general than the classical one of Métivier and Pellaumail. Those notions are associated with some subspace χ of the dual of the projective tensor product of B with itself. We also introduce the notion of a convolution type ...

Banach space valued ultradistributions and applications to abstract Cauchy problems

We define the convolution of Banach space valued ultradistributions in the sense of Braun, Meise, and Taylor. We then treat abstract Cauchy problems in Banach spaces as convolution equations and give a characterization of those problems that have ultradistributional fundamental solutions. Our characterization extends in the Beurling case a result due to H.A. Emamirad. We apply our result to dif...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

New iterative methods with seventh-order convergence for solving nonlinear equations

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.