STABILITY OF THE MULTI-JENSEN EQUATION

Title & Authors
STABILITY OF THE MULTI-JENSEN EQUATION
Prager, Wolfgang; Schwaiger, Jens;

Abstract
Given an $\small{m{\in}\mathbb{N}}$ and two vector spaces V and W, a function f : $\small{V^m{\rightarrow}W}$ is called multi-Jensen if it satisfies Jensen`s equation in each variable separately. In this paper we unify these m Jensen equations to obtain a single functional equation for f and prove its stability in the sense of Hyers-Ulam, using the so-called direct method.
Keywords
stability;multi-Jensen functions;
Language
English
Cited by
1.
ON MULTI-JENSEN FUNCTIONS AND JENSEN DIFFERENCE,;

대한수학회보, 2008. vol.45. 4, pp.729-737
1.
Stability of the multi-Jensen equation, Journal of Mathematical Analysis and Applications, 2010, 363, 1, 249
2.
Stability of multi-additive mappings in non-Archimedean normed spaces, Journal of Mathematical Analysis and Applications, 2011, 373, 2, 376
3.
Hyers-Ulam Stability of Nonlinear Integral Equation, Fixed Point Theory and Applications, 2010, 2010, 1, 927640
4.
On an equation characterizing multi-cauchy-jensen mappings and its Hyers-Ulam stability, Acta Mathematica Scientia, 2015, 35, 6, 1349
5.
On the stability of multi-Jensen mappings in β-normed spaces, Applied Mathematics Letters, 2012, 25, 11, 1866
6.
Remarks on the Hyers–Ulam stability of some systems of functional equations, Applied Mathematics and Computation, 2012, 219, 8, 4096
7.
Approximate Multi-Jensen, Multi-Euler-Lagrange Additive and Quadratic Mappings in -Banach Spaces, Abstract and Applied Analysis, 2013, 2013, 1
8.
On Some Recent Developments in Ulam's Type Stability, Abstract and Applied Analysis, 2012, 2012, 1
9.
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
10.
Existence, uniqueness and stability of solutions for a class of nonlinear integral equations under generalized Lipschitz condition, Indian Journal of Pure and Applied Mathematics, 2012, 43, 4, 309
11.
Stability of multi-additive mappings in -Banach spaces, Nonlinear Analysis: Theory, Methods & Applications, 2012, 75, 11, 4205
12.
Stability of multi-Jensen mappings in non-Archimedean normed spaces, Journal of Mathematical Physics, 2012, 53, 2, 023507
13.
Solution and Stability of the Multiquadratic Functional Equation, Abstract and Applied Analysis, 2013, 2013, 1
14.
On a Jensen-cubic functional equation and its Hyers–Ulam stability, Acta Mathematica Sinica, English Series, 2015, 31, 12, 1929
15.
Approximation solution of nonlinear Stratonovich Volterra integral equations by applying modification of hat functions, Journal of Computational and Applied Mathematics, 2016, 302, 272
16.
Jensen, multi-Jensen and polynomial functions on arbitrary abelian groups, Aequationes mathematicae, 2010, 80, 1-2, 209
17.
Some remarks on the stability of the multi-Jensen equation, Open Mathematics, 2013, 11, 5
18.
Generalized stability of multi-additive mappings, Applied Mathematics Letters, 2010, 23, 10, 1291
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

2.
S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Co., Inc., River Edge, NJ, 2002

3.
G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143-190

4.
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