Semilocal convergence of Stirling's method for fixed points in Banach spaces
by D.K. Gupta; S.K. Parhi; Sukhjit Singh
International Journal of Mathematics in Operational Research (IJMOR), Vol. 9, No. 2, 2016

Abstract: The aim of this paper is to discuss the semilocal convergence of Stirling's method used to find fixed points of nonlinear operator equations in Banach spaces. This convergence is achieved using recurrence relations under the assumption that the first Fréchet derivative of the involved operator satisfies the ω-continuity condition. The ω-continuity condition relaxes the Lipschitz/Hölder continuity condition on the first Frèchet derivative and is given by ||F′ (x) - F′ (y)|| ≤ ω || x - y|| ∀x, y ∈ Ω; where ω R₊ → R₊ is a continuous and non-decreasing function such that ω(0)≥ 0. This work has importance as it does not require the evaluation of second order Fréchet derivative and successfully works for examples for which Lipschitz/Hölder continuity condition on the first Fréchet derivative may fail. A priori error bounds along with the domains of existence and uniqueness for a fixed point are derived. Finally, two numerical examples involving integral equations of Fredholm types are worked out and the results obtained are compared with those obtained by Newton's method. It is found that our approach gives better existence and uniqueness domains for both the examples considered. However, a priori error bounds for our approach are better in one example but not so good in another.

Online publication date: Sun, 31-Jul-2016

The full text of this article is only available to individual subscribers or to users at subscribing institutions.

 
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.

Pay per view:
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.

Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Mathematics in Operational Research (IJMOR):
Login with your Inderscience username and password:

Username:        Password:          Forgotten your password?

Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.

If you still need assistance, please email subs@inderscience.com