HYERS-ULAM-RASSIAS STABILITY OF THE BANACH SPACE VALUED LINEAR DIFFERENTIAL EQUATIONS y′

Title & Authors
HYERS-ULAM-RASSIAS STABILITY OF THE BANACH SPACE VALUED LINEAR DIFFERENTIAL EQUATIONS y′
Miura, Takeshi Miura; Jung, Soon-Mo; Takahasi, Sin-Ei;

Abstract
The aim of this paper is to prove the stability in the sense of Hyers-Ulam- Rassias of the Banach space valued differentialequation y`
Keywords
Hyers-Ulam-Rassias stability;differential equation;
Language
English
Cited by
1.
APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C*-TERNARY ALGEBRAS,;;

대한수학회보, 2010. vol.47. 1, pp.195-209
2.
ON HYERS-ULAM STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS,;;;

대한수학회보, 2015. vol.52. 2, pp.685-697
1.
Approximation of Analytic Functions by Chebyshev Functions, Abstract and Applied Analysis, 2011, 2011, 1
2.
ON HYERS-ULAM STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS, Bulletin of the Korean Mathematical Society, 2015, 52, 2, 685
3.
Bessel's Differential Equation and Its Hyers-Ulam Stability, Journal of Inequalities and Applications, 2007, 2007, 1, 021640
4.
Hyers–Ulam stability with respect to gauges, Journal of Mathematical Analysis and Applications, 2017, 453, 1, 620
5.
On the stability of the heat equation with an initial condition, Journal of Inequalities and Applications, 2013, 2013, 1, 475
6.
Hyers–Ulam stability of a system of first order linear differential equations with constant coefficients, Journal of Mathematical Analysis and Applications, 2006, 320, 2, 549
7.
Hyers–Ulam stability of linear differential equations of first order, Applied Mathematics Letters, 2008, 21, 10, 1024
8.
The Fixed Point Approach to the Stability of Fractional Differential Equations with Causal Operators, Qualitative Theory of Dynamical Systems, 2016, 15, 1, 3
9.
Approximate perfect differential equations of second order, Advances in Difference Equations, 2012, 2012, 1, 225
10.
Approximation of Analytic Functions by Bessel's Functions of Fractional Order, Abstract and Applied Analysis, 2011, 2011, 1
11.
Hyers-Ulam Stability of the Delay Equationy'(t)=λy(t-τ), Abstract and Applied Analysis, 2010, 2010, 1
12.
Hyers–Ulam stability of linear differential equations of first order, III, Journal of Mathematical Analysis and Applications, 2005, 311, 1, 139
13.
On Some Recent Developments in Ulam's Type Stability, Abstract and Applied Analysis, 2012, 2012, 1
14.
Simple Harmonic Oscillator Equation and Its Hyers-Ulam Stability, Journal of Function Spaces and Applications, 2012, 2012, 1
15.
An approximation property of simple harmonic functions, Journal of Inequalities and Applications, 2013, 2013, 1, 3
16.
Invariance of Hyers-Ulam stability of linear differential equations and its applications, Advances in Difference Equations, 2015, 2015, 1
17.
On Approximate Euler Differential Equations, Abstract and Applied Analysis, 2009, 2009, 1
18.
Power series method and approximate linear differential equations of second order, Advances in Difference Equations, 2013, 2013, 1, 76
19.
Stability of linear differential equations of third order, Applied Mathematics Letters, 2011, 24, 11, 1827
20.
An approximation property of exponential functions, Acta Mathematica Hungarica, 2009, 124, 1-2, 155
21.
Hyers–Ulam stability of linear partial differential equations of first order, Applied Mathematics Letters, 2009, 22, 1, 70
22.
On the Stability of Heat Equation, Abstract and Applied Analysis, 2013, 2013, 1
23.
A Fixed Point Approach to the Stability of Linear Differential Equations, Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38, 2, 855
24.
Hyers–Ulam stability of linear differential equations of first order, II, Applied Mathematics Letters, 2006, 19, 9, 854
25.
Legendre's Differential Equation and Its Hyers-Ulam Stability, Abstract and Applied Analysis, 2007, 2007, 1
26.
Implicit function theorem and its application to a Ulam’s problem for exact differential equations, Acta Mathematica Sinica, English Series, 2010, 26, 11, 2085
27.
On the stability of Laplace’s equation, Applied Mathematics Letters, 2013, 26, 5, 549
28.
Ulam’s problem for approximate homomorphisms in connection with Bernoulli’s differential equation, Applied Mathematics and Computation, 2007, 187, 1, 223
29.
Fixed-point results and the Hyers–Ulam stability of linear equations of higher orders, Pacific Journal of Mathematics, 2015, 273, 2, 483
30.
Approximation of analytic functions by bessel functions of fractional order, Ukrainian Mathematical Journal, 2012, 63, 12, 1933
References
1.
C. Alsina and R. Ger, On some inequalities and stability results related to the exponential function, J. Inequal. Appl. 2 (1998), 373–380.

2.
Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), 431–434.

3.
D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222–224.

4.
S.-M. Jung and K. Lee, Hyers-Ulam-Rassias stability of linear differential equations, to appear.

5.
T. Miura, S. Miyajima and S.-E. Takahasi, Hyers-Ulam stability of linear differential operator with constant coefficients, Math. Nachr. 258 (2003), 90–96.

6.
T. Miura, S. Miyajima and S.-E. Takahasi, A characterization of Hyers-Ulam stability of first order linear differential operators, J. Math. Anal. Appl. 286 (2003), 136–146.

7.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.

8.
Th. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989–993.

9.
W. Rudin, Real and Complex Analysis (3rd Edition), McGraw-Hill, 1987.

10.
S.-E. Takahasi, T. Miura and S. Miyajima, On the Hyers-Ulam stability of the Banach space-valued differential equation y' = $\lambda$y, Bull. Korean Math. Soc. 39 (2002), 309–315.

11.
S. M. Ulam, Problems in Modern Mathematics, Chap. VI, Science Editions, Wiley, New York, 1964.

12.
S. M. Ulam, Sets, Numbers and Universes Selected Works, Part III, MIT Press, Cambridge, MA, 1974.