Browse > Article
http://dx.doi.org/10.4134/BKMS.2006.43.1.107

HYERS-ULAM STABILITY OF A CLOSED OPERATOR IN A HILBERT SPACE  

Hirasawa Go (DEPARTMENT OF MATHEMATICS, NIPPON INSTITUTE OF TECHNOLOGY, MIYASHIRO)
Miura Takeshi (DEPARTMENT OF BASIC TECHNOLOGY, APPLIED MATHEMATICS AND PHYSICS, YAMAGATA UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.43, no.1, 2006 , pp. 107-117 More about this Journal
Abstract
We give some necessary and sufficient conditions in order that a closed operator in a Hilbert space into another have the Hyers-Ulam stability. Moreover, we prove the existence of the stability constant for a closed operator. We also determine the stability constant in terms of the lower bound.
Keywords
Hyers-Ulam stability; closed operator;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 4
연도 인용수 순위
1 O. Hatori, K. Kobayashi, T. Miura, H. Takagi, and S. -E. Takahasi, On the best constant of Hyers-Ulam stability, J. Nonlinear Convex Anal. 5 (2004), no. 3, 387-393
2 D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224
3 S. -M. Jung, Hyers-Ulam-Rassias stability of functional equations in mathemat- ical analysis, Hadronic Press, Inc., Florida, 2001
4 T. Miura, S. Miyajima, and S. -E. Takahasi, Hyers-Ulam stability of linear differential operator with constant coefficients, Math. Nachr. 258 (2003), 90-96   DOI   ScienceOn
5 T. Miura, S. Miyajima, and S. -E. Takahasi, A characterization of Hyers-Ulam stability of first order linear differen- tial operators, J. Math. Anal. Appl. 286 (2003), no. 1, 136-146   DOI   ScienceOn
6 Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), no. 1, 264-284   DOI   ScienceOn
7 Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), no. 1, 23-130   DOI
8 Th. M. Rassias, The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), no. 2, 352-378   DOI   ScienceOn
9 Th. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), no. 4, 989-993
10 H. Takagi, T. Miura, and S. -E. Takahasi, Essential norms and stability constants of weighted composition operators on C(X), Bull. Korean Math. Soc. 40 (2003), no. 4, 583-591   DOI   ScienceOn
11 S. -E. Takahasi, H. Takagi, T. Miura, and S. Miyajima, The Hyers-Ulam stability constants of first order linear differential operators, J. Math. Anal. Appl. 296 (2004), no. 2, 403-409   DOI   ScienceOn
12 K. Yosida, Functional analysis, Springer-Verlag, Berlin-New York, 1978
13 Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), no. 3, 431-434   DOI   ScienceOn
14 D. H. Hyers, G. Isac, and Th. M. Rassias, On the asymptoticity aspect of Hyers- Ulam stability of mappings, Proc. Amer. Math. Soc. 126 (1998), no. 2, 425-430
15 S. M. Ulam, A collection of mathematical problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience Publishers, New York-London, 1960
16 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300
17 D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153   DOI