Öz
Sabit nokta yöntemlerini kullanarak, μf((x+y)/2)+μf((x-y)/2)=f(μx) ile tanımlı Jensen tipi fonksiyonel denklem için Jordan k-∗-türevlerinin Γ*-Banach cebirleri üzerindeki stabilitesini ve süper stabilitesini kanıtlıyoruz. Burada μ sayısı, |μ| = 1 şartını sağlayan bir karmaşık sayıdır. Ayrıca, Γ*-Banach cebirleri üzerindeki f(2μx+μy)+f(μx+2μy)=μ[f(3x)+f(3y)] fonksiyonel denklemi ile Jordan k-∗-türevlerinin stabilitesini ve süper stabilitesini araştırıyoruz.
Anahtar Kelimeler
İnvolüsyonlu Γ-halkaları Hyers-Ulam-Rassias stabilitesi Jordan k-*-türevler.
Kaynakça
- Ulam, S.M., Problems in modern mathematics, Chapter VI, science ed. Wiley, New York, (1940).
- Hyers, D.H., On the stability of the linear functional equation, Proceedings of the National Academy of Sciences of the United States of America, 27, 222-224, (1941).
- Rassias, Th. M., On the stability of the linear mapping in Banach spaces, Proceedings of the American Mathematical Society, 72, 297-300, (1978).
- Hyers, D.H., Isac, G. ve Rassias, Th.M., Stability of functional equations in several variables, Birkhauser, Basel, (1998).
- Czerwik, S., Functional equations and inequalities in several variables, River Edge, NJ: World Scientific, (2002).
- Jung, S.M., Hyers-Ulam-Rassias stability of functional equations in mathematical analysis, Palm Harbor: Hadronic Press, (2001).
- Semrl, P., The functional equation of multiplicative derivation is superstable on standard operator algebras, Integral Equations and Operator Theory, 18, 118-122, (1994).
- An, J., Cui, J. ve Park, C., Jordan ∗-derivations on C∗-algebras and JC∗-algebras, Abstract Applied Analysis, Article ID 410437, 1-12, (2008).
- Jang, S. ve Park, C., Approximate ∗-derivations and approximate quadratic ∗-derivations on C∗-algebras, Journal of Inequalities and Applications, Article ID 55, 1-13 pages, (2011).
- Park, C. ve Bodaghi, A., On the stability of ∗-derivations on Banach ∗-algebras, Advances in Differential Equations, 55, 1-10, (2012).
- Nobusawa, N. On the generalization of the ring theory, Osaka Journal of Mathematics, 1, 81-89, (1964).
- Barnes, W.E., On the Γ-rings of Nobusawa, Pacific Journal of Mathematics, 18, 3, 411-422, (1966).
- Sapanci, M. ve Nakajima, A., Jordan derivations on completely prime Γ-rings, Mathematica Japonica, 46, 1, 47-51, (1997).
- Kandamar, H., The k-derivation of a Gamma ring, Turkish Journal of Mathematics, 24, 221-231, (2000).
- Bhattacharya, D.K. ve Maity, A.K., Semilinear tensor product of Gamma Banach algebras, Ganita, 40, 78-80, (1989).
- Hoque, M.F., Alshammari, F.S. ve Paul, A.C., Left centralizers of semiprime Γ-rings with involution, Applied Mathematical Sciences, 95, 4713-4722, (2014).
- Park, C., Homomorphisms between Poisson JC∗-algebras, Bulletin of the Brazilian Mathematical Society, 36, 1, 79-97, (2005).
- Caˇdariu, L. ve Radu, V., On the stability of the Cauchy functional equation: a fixed point approach, Grazer Mathematische Berichte, 346, 43-52, (2004).
- Arslan, B. ve Arslan, O., On the stability of homomorphisms and k-derivations on Gamma-Banach algebras, University Politehnica of Bucharest Scientific Bulletin Series A, 80, 2, 69-78, (2018).
- Najati, A. ve Park, C., Stability of homomorphisms and generalized derivations on Banach algebras, Journal of Inequalities and Applications, 2009, 1-12, (2009).
Öz
Using fixed point methods, we prove the stability and the superstability of Jordan k-∗-derivations on Γ∗-Banach algebras for the following Jensen-type functional equation μf((x+y)/2)+μf((x-y)/2)=f(μx) where μ is a complex number such that |μ| = 1. We also investigate the stability and the superstability of Jordan k-∗-derivations with the functional equation f(2μx+μy)+f(μx+2μy)=μ[f(3x)+f(3y)] on Γ∗-Banach algebras.
Anahtar Kelimeler
Γ-rings with involution Hyers-Ulam-Rassias stability Jordan k-∗-derivations.
Kaynakça
- Ulam, S.M., Problems in modern mathematics, Chapter VI, science ed. Wiley, New York, (1940).
- Hyers, D.H., On the stability of the linear functional equation, Proceedings of the National Academy of Sciences of the United States of America, 27, 222-224, (1941).
- Rassias, Th. M., On the stability of the linear mapping in Banach spaces, Proceedings of the American Mathematical Society, 72, 297-300, (1978).
- Hyers, D.H., Isac, G. ve Rassias, Th.M., Stability of functional equations in several variables, Birkhauser, Basel, (1998).
- Czerwik, S., Functional equations and inequalities in several variables, River Edge, NJ: World Scientific, (2002).
- Jung, S.M., Hyers-Ulam-Rassias stability of functional equations in mathematical analysis, Palm Harbor: Hadronic Press, (2001).
- Semrl, P., The functional equation of multiplicative derivation is superstable on standard operator algebras, Integral Equations and Operator Theory, 18, 118-122, (1994).
- An, J., Cui, J. ve Park, C., Jordan ∗-derivations on C∗-algebras and JC∗-algebras, Abstract Applied Analysis, Article ID 410437, 1-12, (2008).
- Jang, S. ve Park, C., Approximate ∗-derivations and approximate quadratic ∗-derivations on C∗-algebras, Journal of Inequalities and Applications, Article ID 55, 1-13 pages, (2011).
- Park, C. ve Bodaghi, A., On the stability of ∗-derivations on Banach ∗-algebras, Advances in Differential Equations, 55, 1-10, (2012).
- Nobusawa, N. On the generalization of the ring theory, Osaka Journal of Mathematics, 1, 81-89, (1964).
- Barnes, W.E., On the Γ-rings of Nobusawa, Pacific Journal of Mathematics, 18, 3, 411-422, (1966).
- Sapanci, M. ve Nakajima, A., Jordan derivations on completely prime Γ-rings, Mathematica Japonica, 46, 1, 47-51, (1997).
- Kandamar, H., The k-derivation of a Gamma ring, Turkish Journal of Mathematics, 24, 221-231, (2000).
- Bhattacharya, D.K. ve Maity, A.K., Semilinear tensor product of Gamma Banach algebras, Ganita, 40, 78-80, (1989).
- Hoque, M.F., Alshammari, F.S. ve Paul, A.C., Left centralizers of semiprime Γ-rings with involution, Applied Mathematical Sciences, 95, 4713-4722, (2014).
- Park, C., Homomorphisms between Poisson JC∗-algebras, Bulletin of the Brazilian Mathematical Society, 36, 1, 79-97, (2005).
- Caˇdariu, L. ve Radu, V., On the stability of the Cauchy functional equation: a fixed point approach, Grazer Mathematische Berichte, 346, 43-52, (2004).
- Arslan, B. ve Arslan, O., On the stability of homomorphisms and k-derivations on Gamma-Banach algebras, University Politehnica of Bucharest Scientific Bulletin Series A, 80, 2, 69-78, (2018).
- Najati, A. ve Park, C., Stability of homomorphisms and generalized derivations on Banach algebras, Journal of Inequalities and Applications, 2009, 1-12, (2009).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Erken Görünüm Tarihi | 6 Ocak 2024 |
| Yayımlanma Tarihi | 19 Ocak 2024 |
| Gönderilme Tarihi | 21 Mayıs 2023 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 26 Sayı: 1 |