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Extension of Homomorphisms-Isomorphisms and Derivatives on Quasi-Banach Algebra Based on the General Additive Cauchy-Jensen Equation

DOI: 10.4236/oalib.1110095, PP. 1-22

Subject Areas: Mathematics

Keywords: Generalized Additive Equation Cauchy-Jensen Additive, Homomorphisms, Isomorphism and Derivatives on Quasi-Banach Algebra, Quasi-Normed Algebras, p-Banach Algebras

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Abstract

In this paper, I establish homomorphisms, isomorphisms, and derivatives of quasi-algebras based on the general additive equation Cauchy-Jensen with 3k variables. First, I establish the homomorphisms for Equation (1.1); second, I establish the isomorphisms for Equation (1.2); and finally, I develop the derivative for Equation (1.3). These are the main results of this paper.

Cite this paper

An, L. V. (2023). Extension of Homomorphisms-Isomorphisms and Derivatives on Quasi-Banach Algebra Based on the General Additive Cauchy-Jensen Equation. Open Access Library Journal, 10, e095. doi: http://dx.doi.org/10.4236/oalib.1110095.

References

[1]  Ulam, S.M. (1960) A Collection of the Mathematical Problems. Interscience, New York.
[2]  Hyers, D.H. (1941) On the Stability of the Linear Functional Equation. Proceedings of the National Academy of Sciences of the United States of America, 27, 222-224. https://doi.org/10.1073/pnas.27.4.222
[3]  Rassias, T.M. (1978) On the Stability of the Linear Mapping in Banach Spaces. Proceedings of the American Mathematical Society, 72, 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
[4]  Rassias, J.M. (1982) On Approximation of Approximately Linear Mappings by Linear Mappings. Journal of Functional Analysis, 46, 126-130. https://doi.org/10.1016/0022-1236(82)90048-9
[5]  Rassias, J.M. (1984) On Approximation of Approximately Linear Mappings by Linear Mappings. Bulletin des Sciences Mathématiques, 108, 445-446.
[6]  Rassias, J.M. (1989) Solution of a Problem of Ulam. Journal of Approximation Theory, 57, 268-273. https://doi.org/10.1016/0021-9045(89)90041-5
[7]  Găvruta, P. (1994) A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings. Journal of Mathematical Analysis and Applications, 184, 431-436. https://doi.org/10.1006/jmaa.1994.1211
[8]  An, L.V. (2021) Generalized Hyers-Ulam-Rassias Type Stability of the Isometric Additive Mapping in Quasi-Banach Spaces. International Journal of Mathematics Trends and Technology (IJMTT), 67, 31-45. https://doi.org/10.14445/22315373/IJMTT-V67I9P505
[9]  An, L.V. (2021) Generalized Hyers-Ulam-Rassias Type Stability of the Homomrphisms in Quasi-Banach Spaces. Bulletin of Mathematics and Statistics Research, 9, 29-43. http://bomsr.com/9.3.21/29-43%20LY%20VAN%20AN.pdf
[10]  Baak, C. (2006) Cauchy-Rassias Stability of Cauchy-Jensen Additive Mappings in Banach Spaces. Acta Mathematica Sinica, 22, 1789-1796. https://doi.org/10.1007/s10114-005-0697-z
[11]  An, L.V. (2022) Generalized Approximation Hyers-Ulam-Rassias Type Stability of Generalized Homomorphisms in Quasi-Banach Algebras. Asia Mathematika, 6, 7-19. https://www.asiamath.org/
[12]  An, L.V. (2020) Generalized Hyers-Ulam Type Stability of the Additive Functional Equation Inequalities with 2n-Variables on an Approximate Group and Ring Homomorphism. Asia Mathematika, 4, 161-175. http://www.asiamath.org/
[13]  Rolewicz, S. (1984) Metric Linear Spaces. Polish Scientific Publishers, Dordrecht.
[14]  Benyamini, Y. and Lindenstrauss, J. (2000) Geometric Nonlinear Functional Analysis: Volume 1. In: Colloquium Publications, Vol. 48, American Mathematical Society Colloquium Publications, Providence. https://doi.org/10.1090/coll/048
[15]  Aoki, T. (1950) On the Stability of the Linear Transformation in Banach Space. Journal of the Mathematical Society of Japan, 2, 64-66. https://doi.org/10.2969/jmsj/00210064
[16]  Bahyrycz, A. and Piszczek, M. (2014) Hyperstability of the Jensen Functional Equation. Acta Mathematica Hungarica, 142, 353-365. https://doi.org/10.1007/s10474-013-0347-3
[17]  Boo, D.-H., Oh, S.-Q., Park, C.-G. and Park, J.-M. (2003) Generalized Jensen’s Equations in Banach Modules over a C*-Algebra and Its Unitary Group. Taiwanese Journal of Mathematics, 7, 641-655. https://doi.org/10.11650/twjm/1500407583
[18]  Elhoucien, E. and Youssef, M. (2012) On the Paper by A. Najati and S.-M. Jung: The Hyers-Ulam Stability of Approximately Quadratic Mapping on Restricted Domains. Journal of Nonlinear Analysis and Application, 2012, Article ID: Jnaa-00127. https://doi.org/10.5899/2012/jnaa-00127
[19]  Park, C.-G. (2002) On the Stability of the Linear Mapping in Banach Modules. Journal of Mathematical Analysis and Applications, 275, 711-720. https://doi.org/10.1016/S0022-247X(02)00386-4
[20]  Park, C.-G. (2004) Lie *-Homomorphisms between Lie C*-Algebras and Lie *-Derivations on Lie C*-Algebras. Journal of Mathematical Analysis and Applications, 293, 419-434. https://doi.org/10.1016/j.jmaa.2003.10.051
[21]  Park, C.-G. (2005) Homomorphisms between Poisson JC*-Algebras. Bulletin of the Brazilian Mathematical Society, 36, 79-97. https://doi.org/10.1007/s00574-005-0029-z
[22]  Park, C.-G. (2006) Completion of Quasi-Normed Algebras and Quasi-Normed Modules. Journal of the Chungcheong Mathematical Society, 19, 9-18.
[23]  Park, C.-G. (2006) Hyers-Ulam-Rassias Stability of a Generalized Euler-Lagrange Type Additive Mapping and Isomorphisms between C*-Algebras. Bulletin of the Belgian Mathematical Society-Simon Stevin, 13, 619-631. https://doi.org/10.36045/bbms/1168957339
[24]  An, L.V. (2023) Construc the General Jensen-Cauchy Equations in Banach Space and Using Fixed Point Method to Establish Homomorphisms in Banach Algebras. Open Access Library Journal, 10, e9931. https://doi.org/10.4236/oalib.1109931

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