• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.159-175
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• 2006

This paper is a survey on the Hyers-Ulam-Rassias stability of the Jensen functional equation in $C^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Its content is divided into the following sections: 1. Introduction and preliminaries. 2. Approximate isomorphisms in $C^*$-algebras. 3. Approximate isomorphisms in Lie $C^*$-algebras. 4. Approximate isomorphisms in $JC^*$-algebras. 5. Stability of derivations on a $C^*$-algebra. 6. Stability of derivations on a Lie $C^*$-algebra. 7. Stability of derivations on a $JC^*$-algebra.

• Smart Media Journal
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• v.9 no.2
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• pp.33-38
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• 2020

Order preserving matching refers to the problem of reporting substrings of a given text where there exists order isomorphism with the pattern. In this paper, we propose a new algorithm based on filtering and evaluation. The proposed algorithm is simple and easy to implement, and runs in linear time on average. Experimental results show that it works efficiently with real world data.