On stability of some functional equations and topology of their target spaces

Zenon Moszner

Abstract


Some remarks about the coherence of the stability of several functional equations with topology of their target spaces are given. The equations in question are: homogeneity (first of all) and quadratic ones, as well as those of Drygas, Jensen and Schröder. Moreover, we prove, by method different than those used in earlier papers, the superstability of the following equations: Dhombres’, Lobachevski’s and Mikusiński’s ones and those of cosine, sine and of homomorphisms.

Keywords


stability; superstability; functional equation; pertinent target space

Mathematics Subject Classification


39B82, 39B62

References


Alexiewicz, A. "Analiza funkcjonalna." Monografie Matematyczne 49. Warszawa: PWN, 1969.

Baker, J.A. "The stability of the cosine equation." Proc. Amer. Math. Soc. 80 (1980): 411-416.

Batko, B. "Stability of Dhombres’ equation." Bull. Austral. Math. Soc. 70 (2004): 499-505.

---. "Note on superstability of Mikusinski’s functional equation." Functional Equations in Mahematical Analysis. Springer, 2012. 15-17.

Cholewa, P.W. "The stability of the sine equation." Proc. Amer. Math. Soc. 88 (1983): 631-634.

Czerwik, S. :Functional equations and inequalities in several variables." River Edge, NJ: World Scientific Publishing Co., Inc., 2002.

Forti, G.L. and J. Schwaiger. "Stability of homomorphisms and completeness." C. R. Math. Rep. Acad. Sci. Canada 11 (1989): 215-220.

Găvruta, P. "On the stability of some functional equations." Stability of mappings of Hyers-Ulam type 93-98. Palm Harbor, FL: Hadronic Press Collect. Orig. Artic., Hadronic Press, 1994.

Hyers, D.H. "On the stability of the linear functional equation." Proc. Nat. Acad. Sci. USA 27 (1941): 222-224.

Jabłoński, W. and J. Schwaiger. "Stability of the homogeneity and completeness." Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 214 (2005): 111-132.

Moszner, Z. "Stability of the equation of homomorphim and completeness of the underlying space." Opuscula Math. 28 (2008): 83-92.

Skof, F. "Proprieta locali e approssimazione di operatori." Rend. Sem. Mat. Fis. Milano 53 (1983): 113-129.

Yang, D. "Remarks on the stability of Drygas’ equation and the Pexider-quadartic equation." Aequationes Math. 68 (2004): 108-116.

Żelazko, W. "Metric generalizations of Banach algebras." Rozprawy Mat. 47, 1965.

---. "Algebry Banacha."Warszawa: PWN, 1968.


Full Text: PDF

Download statistics: 2619



e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej