JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON MULTI-JENSEN FUNCTIONS AND JENSEN DIFFERENCE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON MULTI-JENSEN FUNCTIONS AND JENSEN DIFFERENCE
Cieplinski, Krzysztof;
  PDF(new window)
 Abstract
In this paper we characterize multi-Jensen functions f : , where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : is Borel measurable, we obtain representation of f (respectively, f, g, h : ) such that the Jensen difference (respectively, the Pexider difference takes values in a countable subgroup of .
 Keywords
multi-Jensen function;multi-additive mapping;stability;Jensen difference;Pexider difference;
 Language
English
 Cited by
1.
On the stability of multi-Jensen mappings in β-normed spaces, Applied Mathematics Letters, 2012, 25, 11, 1866  crossref(new windwow)
2.
Stability of the multi-Jensen equation, Journal of Mathematical Analysis and Applications, 2010, 363, 1, 249  crossref(new windwow)
3.
On an equation characterizing multi-cauchy-jensen mappings and its Hyers-Ulam stability, Acta Mathematica Scientia, 2015, 35, 6, 1349  crossref(new windwow)
4.
On Some Recent Developments in Ulam's Type Stability, Abstract and Applied Analysis, 2012, 2012, 1  crossref(new windwow)
5.
Stability of multi-Jensen mappings in non-Archimedean normed spaces, Journal of Mathematical Physics, 2012, 53, 2, 023507  crossref(new windwow)
6.
Solution and Stability of the Multiquadratic Functional Equation, Abstract and Applied Analysis, 2013, 2013, 1  crossref(new windwow)
7.
Remarks on the Hyers–Ulam stability of some systems of functional equations, Applied Mathematics and Computation, 2012, 219, 8, 4096  crossref(new windwow)
8.
Generalized stability of multi-additive mappings, Applied Mathematics Letters, 2010, 23, 10, 1291  crossref(new windwow)
9.
Approximate Multi-Jensen, Multi-Euler-Lagrange Additive and Quadratic Mappings in -Banach Spaces, Abstract and Applied Analysis, 2013, 2013, 1  crossref(new windwow)
10.
Stability of multi-additive mappings in -Banach spaces, Nonlinear Analysis: Theory, Methods & Applications, 2012, 75, 11, 4205  crossref(new windwow)
11.
On an equation characterizing multi-Jensen-quadratic mappings and its Hyers–Ulam stability via a fixed point method, Journal of Fixed Point Theory and Applications, 2016, 18, 4, 737  crossref(new windwow)
12.
Stability of multi-additive mappings in non-Archimedean normed spaces, Journal of Mathematical Analysis and Applications, 2011, 373, 2, 376  crossref(new windwow)
13.
Jensen, multi-Jensen and polynomial functions on arbitrary abelian groups, Aequationes mathematicae, 2010, 80, 1-2, 209  crossref(new windwow)
14.
Some remarks on the stability of the multi-Jensen equation, Open Mathematics, 2013, 11, 5  crossref(new windwow)
 References
1.
J.-H. Bae and W.-G. Park, On the solution of a bi-Jensen functional equation and its stability, Bull. Korean Math. Soc. 43 (2006), no. 3, 499-507 crossref(new window)

2.
M. Bajger, On the composite Pexider equation modulo a subgroup, Publ. Math. Debrecen 64 (2004), no. 1-2, 39-61

3.
K. Baron, Orthogonality and additivity modulo a discrete subgroup, Aequationes Math. 70 (2005), no. 1-2, 189-190 crossref(new window)

4.
K. Baron and Pl. Kannappan, On the Pexider difference, Fund. Math. 134 (1990), no. 3, 247-254

5.
J. Brzdek, The Cauchy and Jensen diferences on semigroups, Publ. Math. Debrecen 48 (1996), no. 1-2, 117-136

6.
J. Brzdek, On orthogonally exponential functionals, Pacific J. Math. 181 (1997), no. 2, 247-267 crossref(new window)

7.
L. Cadariu and V. Radu, Fixed points and the stability of Jensen's functional equation, JIPAM. J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Article 4

8.
K. Cieplinski, On a generalized Pexider equation and the Pexider difference, Iteration theory (ECIT '06), 27-36, Grazer Math. Ber., 351, Karl-Franzens-Univ. Graz, Graz, 2007

9.
J. G. van der Corput, Goniometrische functies gekarakteriseerd door een functionaal betrekking, Euclides 17 (1940), 55-75

10.
G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143-190 crossref(new window)

11.
N. Frantzikinakis, Additive functions modulo a countable subgroup of $\mathbb{R}$, Colloq. Math. 95 (2003), no. 1, 117-122 crossref(new window)

12.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436 crossref(new window)

13.
P. Gavruta, S.-M. Jung, and K.-S. Lee, Remarks on the Pexider equations modulo a subgroup, Far East J. Math. Sci. (FJMS) 19 (2005), no. 2, 215-222

14.
G. Godini, Set-valued Cauchy functional equation, Rev. Roumaine Math. Pures Appl. 20 (1975), no. 10, 1113-1121

15.
D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of functional equations in several variables, Progress in Nonlinear Differential Equations and their Applications, 34. Birkhaser Boston, Inc., Boston, MA, 1998

16.
K.-W. Jun and Y.-H. Lee, A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation, J. Math. Anal. Appl. 238 (1999), no. 1, 305-315 crossref(new window)

17.
S.-M. Jung, Hyers-Ulam-Rassias stability of Jensen's equation and its application, Proc. Amer. Math. Soc. 126 (1998), no. 11, 3137-3143

18.
S.-M. Jung, On the quadratic functional equation modulo a subgroup, Indian J. Pure Appl. Math. 36 (2005), no. 8, 441-450

19.
S.-M. Jung and K.-S. Lee, On the Jensen functional equation modulo a subgroup, J. Appl. Algebra Discrete Struct. 5 (2007), no. 1, 21-32

20.
Z. Kominek, On a local stability of the Jensen functional equation, Demonstratio Math. 22 (1989), no. 2, 499-507

21.
A. Najati, Hyers-Ulam-Rassias stability of a cubic functional equation, Bull. Korean Math. Soc. 44 (2007), no. 4, 825-840 crossref(new window)

22.
C. Park and Th. M. Rassias, d-isometric linear mappings in linear d-normed Banach modules, J. Korean Math. Soc. 45 (2008), no. 1, 249-271 crossref(new window)

23.
W. Prager and J. Schwaiger, Multi-affine and multi-Jensen functions and their connection with generalized polynomials, Aequationes Math. 69 (2005), no. 1-2, 41-57 crossref(new window)

24.
W. Prager and J. Schwaiger, Stability of the multi-Jensen equation, Bull. Korean Math. Soc. 45 (2008), no. 1, 133-142 crossref(new window)

25.
S. M. Ulam, Problems in Modern Mathematics, Science Editions John Wiley & Sons, Inc., New York, 1964