On the Convergence Region of Multi-step Chebyshev-Halley-type Schemes for Solving Equations

Journal Title: Earthline Journal of Mathematical Sciences - Year 2019, Vol 1, Issue 2

Abstract

The aim of this article is to extend the convergence region of certain multi-step Chebyshev-Halley-type schemes for solving Banach space valued nonlinear equations. In particular, we find an at least as small region as the region of the operator involved containing the iterates. This way the majorant functions are tighter than the ones related to the original region, leading to a finer local as well as a semi-local convergence analysis under the same computational effort. Numerical examples complete this article.

Authors and Affiliations

Ioannis K. Argyros, Santhosh George

Keywords

Related Articles

Further Generalized Beta Function with Three Parameters Mittag-Leffler Function

The purpose of the present paper is to introduce a new extension of extended Beta function by product of two Mittag-Leffler functions. Further, we present certain results including summation formulas, integral representa...

Strong Differential Subordination Results for Multivalent Analytic Functions Associated with Dziok-Srivastava Operator

In this paper, by making use of the principle of strong subordination, we establish some interesting properties of multivalent analytic functions defined in the open unit disk and closed unit disk of the complex plane as...

Insertion of a Contra-continuous Function between Two Comparable Real-valued Functions

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a contra-continuous function between two comparable real-valued functions on such topological spaces that kernel of sets are...

A New Symmetric p-stable Obrechkoff Method with Optimal Phase lag for Oscillatory Problems

In this paper, we derive a class of symmetric p-stable Obrechkoff methods via Padé approximation approach (PAA) for the numerical solution of special second order initial value problems (IVPs) in ordinary differential eq...

On Pretopological Vector Spaces

The purpose of the present paper is to introduce the new class of topological spaces, namely pretopological vector spaces. We study some of the basic properties of pretopological vector spaces and investigate their relat...

Download PDF file
  • EP ID EP481486
  • DOI 10.34198/ejms.1219.187207
  • Views 227
  • Downloads 0

How To Cite

Ioannis K. Argyros, Santhosh George (2019). On the Convergence Region of Multi-step Chebyshev-Halley-type Schemes for Solving Equations. Earthline Journal of Mathematical Sciences, 1(2), 187-207. https://europub.co.uk/articles/-A-481486