Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-07-28T08:43:24.393Z Has data issue: false hasContentIssue false
  • English
  • Français

ON APPROXIMATE SOLUTIONS OF SOME DIFFERENCE EQUATIONS

Part of: Equations and inequalities involving nonlinear operators Difference equations Difference and functional equations Nonlinear operators and their properties

Published online by Cambridge University Press:  01 December 2016

JANUSZ BRZDĘK  and
PAWEŁ WÓJCIK
JANUSZ BRZDĘK
Affiliation:
Institute of Mathematics, Pedagogical University of Cracow, Podchorążych 2, 30-084 Kraków, Poland email jbrzdek@up.krakow.pl
PAWEŁ WÓJCIK*
Affiliation:
Institute of Mathematics, Pedagogical University of Cracow, Podchorążych 2, 30-084 Kraków, Poland email pwojcik@up.krakow.pl
*
✉pwojcik@up.krakow.pl
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we present a simple (fixed point) method that yields various results concerning approximate solutions of some difference equations. The results are motivated by the notion of Ulam stability.

Keywords

Hyers–Ulam stabilitylinear recurrencedifference equationBanach spacemetric spacefixed point theorem

MSC classification

Primary: 39B82: Stability, separation, extension, and related topics
Secondary: 39A06: Linear equations 47H10: Fixed-point theorems 47J05: Equations involving nonlinear operators (general) 47J25: Iterative procedures
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 3 , June 2017 , pp. 476 - 481
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Agarwal, R. P., Xu, B. and Zhang, W., ‘Stability of functional equations in single variable’, J. Math. Anal. Appl. 288 (2003), 852–869.CrossRefGoogle Scholar
Brillouët-Belluot, N., Brzdęk, J. and Ciepliński, K., ‘On some recent developments in Ulam’s type stability’, Abstr. Appl. Anal. 2012 (2012), Article ID 716936, 41 pp.Google Scholar
Brzdęk, J., Popa, D. and Xu, B., ‘The Hyers–Ulam stability of nonlinear recurrences’, J. Math. Anal. Appl. 335 (2007), 443–449.Google Scholar
Brzdęk, J., Popa, D. and Xu, B., ‘Remarks on stability of linear recurrence of higher order’, Appl. Math. Lett. 23 (2010), 1459–1463.CrossRefGoogle Scholar
Brzdęk, J., Popa, D. and Xu, B., ‘On nonstability of the linear recurrence of order one’, J. Math. Anal. Appl. 367 (2010), 146–153.Google Scholar
Jung, S.-M., Popa, D. and Rassias, M. Th., ‘On the stability of the linear functional equation in a single variable on complete metric groups’, J. Global Optim. 59 (2014), 165–171.Google Scholar
Popa, D., ‘Hyers–Ulam–Rassias stability of the general linear equation’, Nonlinear Funct. Anal. Appl. 7 (2002), 581–588.Google Scholar
Popa, D., ‘Hyers–Ulam–Rassias stability of a linear recurrence’, J. Math. Anal. Appl. 309 (2005), 591–597.Google Scholar
Popa, D., ‘Hyers–Ulam stability of the linear recurrence with constant coefficients’, Adv. Difference Equ. 2005 (2005), 101–107.Google Scholar