Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem

• Autores: Mehdi Dehghanian, Choonkil Park, Yamin Sayyari
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 2, 2023, págs. 273-288
• Idioma: inglés
• DOI: 10.56754/0719-0646.2502.273
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En este artículo, introducimos el concepto de antiderivación ternaria en álgebras de Banach ternarias e investigamos la estabilidad de las antiderivaciones ternaria en álgebras de Banach ternarias, asociadas a la (α, β)- desigualdad funcional: ∥F(x + y + z) − F(x + z) − F(y − x + z) − F(x − z)∥ ≤ ∥α(F(x + y − z) + F(x − z) − F(y))∥ + ∥β(F(x − z) + F(x) − F(z))∥ donde α y β son números complejos no cero fijos, con |α| + |β| < 2 usando el método de punto fijo.

  • English

    Abstract In this paper, we introduce the concept of ternary antiderivation on ternary Banach algebras and investigate the stability of ternary antiderivation in ternary Banach algebras, associated to the (α, β)-functional inequality: ∥F(x + y + z) − F(x + z) − F(y − x + z) − F(x − z)∥ ≤ ∥α(F(x + y − z) + F(x − z) − F(y))∥ + ∥β(F(x − z) + F(x) − F(z))∥ where α and β are fixed nonzero complex numbers with |α|+ |β| < 2 by using the fixed point method.

• Referencias bibliográficas
  • Abdollahpoura, M. R.,Aghayaria, R.,Rassias, M. Th.. (2016). Hyers-Ulam stability of associated Laguerre differential equations in a subclass...
  • Brzdęk, J.. (2009). On a method of proving the Hyers-Ulam stability of functional equations on restricted domains. Aust. J. Math. Anal. Appl.....
  • Brzdęk, J.,Cădariu, L.,Ciepliński, K.. (2014). Fixed point theory and the Ulam stability. J. Funct. Spaces. 2014.
  • Brzdęk, J.,Cădariu, L.,Ciepliński, K.,Fošner, A.,Leśniak, Z.. (2016). Survey on recent Ulam stability results concerning derivations. J. Funct....
  • Brzdęk, J.,Ciepliński, K.. (2013). Hyperstability and superstability. Abstr. Appl. Anal.. 2013.
  • Brzdęk, J.,Fošner, A.. (2015). On approximate generalized Lie derivation. Glas. Mat. Ser. III. 50. 77-99
  • Brzdęk, J.,Fošner, A.,Leśniak, Z.. (2020). A note on asymptotically approximate generalized Lie derivations. J. Fixed Point Theory Appl.....
  • Dehghanian, M.,Modarres, S. M. S.. (2012). Ternary γ-homomorphisms and ternary γ-derivations on ternary semigroups. J. Inequal. Appl.. 2012....
  • Dehghanian, M.,Modarres, S. M. S.,Park, C.,Shin, D. Y.. (2013). C∗-Ternary 3-derivations on C∗-ternary algebras. J. Comput. Anal. Appl.. 2013....
  • Dehghanian, M.,Park, C.. (2014). C∗-Ternary 3-homomorphisms on C∗-ternary algebras. Results Math.. 66. 87-98
  • Dehghanian, M.,Sayyari, Y.,Park, C.. (2023). Hadamard homomorphisms and Hadamard derivations on Banach algebras. Miskolc Math. Notes. 24....
  • Diaz, J. B.,Margolis, B.. (1968). A fixed point theorem of the alternative for contractions on a generalized complete metric space. Bull....
  • Habil, E. D.. (2006). Double sequences and double series. Islamic Univ. J. Ser. Nat. Stud. Eng.. 14. 1-32
  • Haddadi, M. R.,Dehghanian, M.. (2018). Existence and convergence theorems for equilibrium problems and fixed point problem. Southeast Asian...
  • Hosseinioun, S. A.,Farrokhzad, R.,Gordj, M. Eshaghi. (2014). Nearly higher ternary derivations in Banach ternary algebras: An alternative...
  • Govindan, V.,Park, C.,Pinelas, S.,Rassias, Th. M.. (2020). Hyers-Ulam stability of an additive-quadratic functional equation. Cubo. 22. 233
  • Hyers, D. H.. (1941). On the stability of the linear functional equation. Proc. Nat. Acad. Sci. U.S.A.. 27. 222
  • Kerner, R.. (2000). Ternary algebraic structures and their applications in physics. Pierre et Marie Curie University, Paris; Proc. BTLP, 23rd...
  • Lü, F.,Guo, H.. (2022). On meromorphic solutions of the Fermat-type functional equation f(z) n + f(z + c) m = e αz+β. Mediterr....
  • Mihet, D.,Radu, V.. (2008). On the stability of the additive Cauchy functional equation in random normed spaces. J. Math. Anal. Appl.. 343....
  • Nambu, Y.. (1973). Generalized Hamiltonian mechanics. Phys. Rev.. 7. 2405
  • Paokanta, S.,Dehghanian, M.,Park, C.,Sayyari, Y.. (2023). A system of additive functional equations in complex Banach algebras. Demonstr....
  • Park, C.. (2005). Homomorphisms between Poisson JC∗-algebras. Bull. Braz. Math. Soc. (N.S.). 36. 79-97
  • Park, C.. (2017). Fixed point method for set-valued functional equations. J. Fixed Point Theory Appl.. 19. 2297
  • Park, C.. (2019). The stability of an additive (ρ1, ρ2)-functional inequality in Banach spaces. J. Math. Inequal.. 13. 95-104
  • Park, C.. (2021). Derivation-homomorphism functional inequality. J. Math. Inequal.. 15. 95-105
  • Sayyari, Y.,Dehghanian, M.,Nasiri, Sh.. (2022). Solution of some irregular functional equations and their stability. J. Linear Topol. Algebra....
  • Sayyari, Y.,Dehghanian, M.,Park, C.. (2023). A system of biadditive functional equations in Banach algebras. Appl. Math. Sci. Eng.. 31.
  • Sayyari, Y.,Dehghanian, M.,Park, C.,Lee, J.. (2022). Stability of hyper homomorphisms and hyper derivations in complex Banach algebras. AIMS...
  • Širovnik, N.. (2014). On certain functional equation in semiprime rings and standard operatoralgebras. Cubo. 16. 73-80