On approximate orthogonally ring homomorphisms and orthogonally ring derivations in Banach algebras with the new type fixed point

Document Type : Research Paper


1 Mathematics Department-College of Science, Islamic Azad University Central Tehran Branch, Tehran, Iran.

2 Department of Mathematics, Semnan University, Semnan, Iran.


In this paper,
Using fixed point methods, we prove the stability of orthogonally ring homomorphism and orthogonally ring derivation in Banach algebras.


[1] N. Ansari, M.H. Hooshmand, M. Eshaghi Gordji, K. Jahedi, Stability of fuzzy orthogonally -n-derivation in orthogonally fuzzy C*-algebras, J. Nonlinear Anal. Appl. 12 (2021) 533{540 .
[2] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950) 64{66.
[3] R. Badora, On approximate derivations, Math. Inequal. Appl. 9 (2006) 167{173.
[4] A. Bahraini, G. Askari, Homogeneous Equation Between Banach -Modules, Journal of Mathematical Analysis 9 (2018) 11{18.
[5] A. Bahraini, G. Askari, M. Eshaghi Gordji, R. Gholami, Stability and hyperstability of orthogonally -m-homomorphisms in orthogonally Lie C-algebras: a  xed point approach , J. Fixed Point Theory Appl. (2018), 1{12.
[6] H. Baghani, M. E. Gordji, M. Ramezani, Orthogonal sets: The axiom of choice and proof of a  xed point theorem, J.  Fixed Point Theory Appl., 18 (2016), 465{477.
[7] M. Bavand Savadkouhi, M.E. Gordji, J.M. Rassias, N. Ghobadipour, Approximate ternary Jordan derivations on Banach ternary algebras, J. Math. Phys. 50 (2009), 20{29.
[8] L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: A  xed point approach, Grazer Math. Ber. 346 (2004).
[9] L. Cadariu, V. Radu, Fixed points and the stability of Jensens functional equation, J. Ineq. Pure Appl. Math. 4 (2003).
[10] L. Cadariu, V. Radu, Fixed Point Methods for the Generalized Stability of Functional Equations in a Single Variabl, Fixed Point Theory Appl. (2008) 1{15.
[11] M. Eshaghi, H. Habibi, Existence and uniqueness of solutions to a  rst-order di erential equation via  xed point theorem in orthogonal metric space, FACTA UNIVERSITATIS (NIS) Ser. Math. 34 (2019) 123-135.
[12] M. Eshaghi Gordji, H Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Topol. Algeb., 6 (2017), 251{260.
[13] M. Eshaghi Gordji, H. Habibi and M.B. Sahabi, Orthogonal sets; orthogonal contractions, Asian-Eur. J. Math. 12 (2019).
[14] M. Eshaghi Gordji, G. Askari, N. Ansari, G. A. Anastassiou and C. Park, Stability and hyperstability of generalized orthogonally quadratic ternary homomorphisms in non-Archimedean ternary Banach algebras: a  xed point approach, J. Computational Analysis And Applications, 21 (2016) 1{8.
[15] M. Eshaghi Gordji, M. Ramezani, M. De La Sen, and Y.J. Cho, On orthogonal sets and Banach  xed point theorem, Fixed Point Theory, 18 (2017), 569{578.
[16] M. Eshaghi Gordji, R. Farokhzad and S. A. R. Hosseinioun, Ternary (; ; )-derivations on Banach ternary algebras, Int. J. Nonlinear Anal. Appl., 5 (2014) 23{35.
[17] R. Farokhzad, S.A.R. Hosseinioun, Perturbations of Jordan higher derivations in Banach ternary algebras: An alternative  xed point approach, Int. J. Nonlinear Anal. Appl. 1 (2010) 42{53.
[18] P. Gavruta, An answer to a question of John M. Rassias concerning the stability of Cauchy equation, In Advances in Equation and Inequalities, Hardronic Math Sel., (1999) 67{71.
[19] P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994) 431{436.
[20] P. Gavruta, L. Gavruta, A new method for the generalized Hyers-Ulam-Rassias stability, Int. J. Nonlinear Anal. Appl. 1 (2010) 11{18.
[21] R. Gholami, G. Askari, M. Eshaghi Gordji, Stability and hyperstability of orthogonally ring -n-derivations and orthogonally ring -n-homomorphisms on C* algebras, J. Linear Topol. Algebra, 7 (2018), 109{119.
[22] H. Hosseini, M. Eshaghi, Fixed Point Results in Orthogonal Modular Metric Spaces, J. Nonlinear Anal. Appl. 11 (2020) 425{436.
[23] D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. 27 (1941) 222{224.
[24] Y.S. Jung, On the generalized Hyers-Ulam stability of module left derivations, J. Math . Anal. Appl. 339 (2008) 108-114.
[25] B. Margolis, J.B. Diaz, A  xed point theorem of the alternative for contractions on the generalized complete metric space, Bull. Amer. Math. Soc. 126 (1968), 305{309.
[26] T. Miura, G. Hirasawa, S.-E. Takahasi, A perturbation of ring derivations on Banach algebras, J. Math. Anal. Appl. 319 (2006) 522{530.
[27] C. Park, M. Eshaghi Gordji, Comment on "Approximate ternary Jordan derivations on Banach ternary algebras Bavand Savadkouhi et al. J. Math. Phys. 50, (2009)] J. Math. Phys. 51 (2010).
[28] G. Polya, G. Szego, Aufgaben und lehrsatze der Analysis, Springer, Berlin, 1925.
[29] V. Radu, The  xed point alternative and the stability of functional equations, Sem. Fixed Point Theory 4 (2003) 91{96.
[30] J.M. Rassias, Complete solution of the multi-dimensional of Ulam, Discuss. Math. 14 (1994) 101{107.
[31] J.M. Rassias, On Approximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982) 126{130.
[32] J.M. Rassias, On stability of the Euler-Lagrange functional equation, Chin. J. Math 20 (1992) 185{190.
[33] Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer.Math. Soc., 72 (1978) 297{300.
[34] J.M. Rassias, Solution of a problem of Ulam, J. Approx. Theory 57 (1989) 268{273.
[35] P.  Semrl, The functional equation of multiplicative derivation is superstable on standard operator algebras, Integral Equations and Operator Theory 18 (1994) 118{122.
[36] S.M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1964.
Volume 10, Issue 2
Special Issue Dedicated to Professor M. Radjabalipour on the occasion of his 75th birthday.
October 2021
Pages 115-124
  • Receive Date: 10 August 2020
  • Revise Date: 04 September 2021
  • Accept Date: 25 September 2021
  • First Publish Date: 01 October 2021