Stabilities of Cubic Mappings in Various Normed Spaces: Direct and Fixed Point Methods
Joint Authors
Talebzadeh, S.
Lee, S. Jin
Azadi Kenary, Hassan
Rezaei, H.
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-28, 28 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-11-23
Country of Publication
Egypt
No. of Pages
28
Main Subjects
Abstract EN
In 1940 and 1964, Ulam proposed the general problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”.
In 1941, Hyers solved this stability problem for linear mappings.
According to Gruber (1978) this kind of stability problems are of the particular interest in probability theory and in the case of functional equations of different types.
In 1981, Skof was the first author to solve the Ulam problem for quadratic mappings.
In 1982–2011, J.
M.
Rassias solved the above Ulam problem for linear and nonlinear mappings and established analogous stability problems even on restricted domains.
The purpose of this paper is the generalized Hyers-Ulam stability for the following cubic functional equation: f(mx+y)+f(mx-y)=mf(x+y)+mf(x-y)+2(m3-m)f(x),m≥2 in various normed spaces.
American Psychological Association (APA)
Azadi Kenary, Hassan& Rezaei, H.& Talebzadeh, S.& Lee, S. Jin. 2011. Stabilities of Cubic Mappings in Various Normed Spaces: Direct and Fixed Point Methods. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-1028928
Modern Language Association (MLA)
Azadi Kenary, Hassan…[et al.]. Stabilities of Cubic Mappings in Various Normed Spaces: Direct and Fixed Point Methods. Journal of Applied Mathematics No. 2012 (2012), pp.1-28.
https://search.emarefa.net/detail/BIM-1028928
American Medical Association (AMA)
Azadi Kenary, Hassan& Rezaei, H.& Talebzadeh, S.& Lee, S. Jin. Stabilities of Cubic Mappings in Various Normed Spaces: Direct and Fixed Point Methods. Journal of Applied Mathematics. 2011. Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-1028928
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1028928