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GENERALIZED QUASI–BANACH SPACES AND QUASI–(2; p)–NORMED SPACES
Choonkil Park 충청수학회 2006 충청수학회지 Vol.19 No.2
In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated. We introduce quasi-2-normed spaces and quasi-(2; p)-normed spaces, and investigate the properties of quasi-2-normed spaces and quasi-(2; p)-normed spaces.
APPROXIMATE RING HOMOMORPHISMS OVER p-ADIC FIELDS
Choonkil Park,Kil-Woung Jun,Gang Lu 충청수학회 2006 충청수학회지 Vol.19 No.3
In this paper, we prove the generalized Hyers–Ulam stability of ring homomorphisms over the p-adic field Q p associated with the Cauchy functional equation f (x+y) = f (x)+f (y) and the Cauchy–Jensen functional equation 2f ( x+y 2 + z) = f (x) + f (y) + 2f (z).
ON THE QUADRATIC MAPPING IN GENERALIZED QUASI-BANACH SPACES
Choonkil Park,Kil-Woung Jun,Gang Lu 충청수학회 2006 충청수학회지 Vol.19 No.3
In this paper, we prove the Hyers–Ulam–Rassias stability of the quadratic mapping in generalized quasi-Banach spaces, and of the quadratic mapping in generalized p-Banach spaces.
GENERALIZED QUASI–BANACH SPACES
Choonkil Baak 충청수학회 2005 충청수학회지 Vol.18 No.2
In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated.
Generalized Quasi-Banach Spaces
Choonkil Baak 충청수학회 2005 충청수학회지 Vol.18 No.2
In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated.
HYERS-ULAM-RASSIAS STABILITY OF ISOMORPHISMS IN C -ALGEBRAS
Choonkil Park 충청수학회 2006 충청수학회지 Vol.19 No.2
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.
HYERS-ULAM-RASSIAS STABILITY OF ISOMORPHISMS IN C<SUP>*</SUP>-ALGEBRAS
Park, Choonkil 충청수학회 2006 충청수학회지 Vol.19 No.2
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.
APPROXIMATE RING HOMOMORPHISMS OVER p-ADIC FIELDS
Park, Choonkil,Jun, Kil-Woung,Lu, Gang 충청수학회 2006 충청수학회지 Vol.19 No.3
In this paper, we prove the generalized Hyers-Ulam stability of ring homomorphisms over the p-adic field $\mathbb{Q}_p$ associated with the Cauchy functional equation f(x+y) = f(x)+f(y) and the Cauchy-Jensen functional equation $2f(\frac{x+y}{2}+z)=f(x)+f(y)+2f(z)$.