## Abstract and Applied Analysis

### About the Local Stability of the Four Cauchy Equations Restricted on a Bounded Domain and of Their Pexiderized Forms

Fulvia Skof

#### Abstract

The Ulam-Hyers stability of functional equations is widely studied from various points of view by many authors. The present paper is concerned with local stability of the four Cauchy equations restricted on a bounded domain. These results can be easily adapted to the corresponding Pexiderized equations.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 380743, 9 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393448668

Digital Object Identifier
doi:10.1155/2013/380743

Mathematical Reviews number (MathSciNet)
MR3143566

Zentralblatt MATH identifier
1291.39056

#### Citation

Skof, Fulvia. About the Local Stability of the Four Cauchy Equations Restricted on a Bounded Domain and of Their Pexiderized Forms. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 380743, 9 pages. doi:10.1155/2013/380743. https://projecteuclid.org/euclid.aaa/1393448668

#### References

• D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, pp. 222–224, 1941.
• D. H. Hyers, “The stability of homomorphisms and related topics,” in Global Analysis-Analysis on Manifolds, M. Th. Rassias, Ed., pp. 140–153, Teubner, Leipzig, Germany, 1983.
• D. H. Hyers and T. M. Rassias, “Approximate homomorphisms,” Aequationes Mathematicae, vol. 44, no. 2-3, pp. 125–153, 1992.
• F. Skof, “Sull'approssimazione delle applicazioni localmente $\delta$-additive,” Atti dell' Accademia delle Scienze di Torino, vol. 117, pp. 337–389, 1983.
• F. Skof, “Local properties and approximation of operators,” Rendiconti del Seminario Matematico e Fisico di Milano, vol. 53, pp. 113–129, 1983.
• N. Brillouët-Belluot, J. Brzd\kek, and K. Ciepliński, “On some recent developments in Ulam's type stability,” Abstract and Applied Analysis, vol. 2012, Article ID 716936, 41 pages, 2012.
• Z. Daróczy and L. Losonczi, “Über die Erweiterung der auf einer Punktmenge additiven Funktionen,” Publicationes Mathematicae Debrecen, vol. 14, pp. 239–245, 1967.
• J. Aczél and F. Skof, “Local Pexider and Cauchy Equations,” Aequationes Mathematicae, vol. 73, no. 3, pp. 311–320, 2007.
• F. Skof, “The general solution of the exponential Cauchy equation on a bounded restricted domain,” Aequationes Mathematicae, vol. 73, no. 1-2, pp. 144–155, 2007.
• F. Skof, “Extension results for restricted Cauchy equations,” Atti dell' Accademia delle Scienze di Torino, vol. 141, pp. 33–42; 51–60, 2007.