Abstract
In this paper, we introduce the concept of Hadamard 𝔇-hom-der on Banach algebras. Further, we apply the fixed point method to prove the stability of the Hadamard 𝔇-hom-der on Banach algebras.
Acknowledgement
We would like to express our sincere gratitude to the anonymous referee for his/her helpful comments that will help to improve the quality of the manuscript.
- (Communicated by Gregor Dolinar) 
References
[1] Bae, J. H.—Park, W. G.: Approximate bi-homomorphisms and bi-derivations in C*-ternary algebras, Bull. Korean Math. Soc. 47(1) (2010), 195–209.Search in Google Scholar
[2] Bodaghi, A.: Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach, Math. Slovaca 71(1) (2021), 117–128.Search in Google Scholar
[3] Dehghanian, M.—Modarres, S. M. S.: Ternary γ-homomorphisms and ternary γ-derivations on ternary semigroups, J. Inequal. Appl. 2012 (2012), Art. No. 34.Search in Google Scholar
[4] Dehghanian, M.—Modarres, S. M. S.—Park, C.—Shin, D. Y.: C*-Ternary 3-derivations on C*-ternary algebras, J. Inequal. Appl. 2013 (2013), Art. No. 124.Search in Google Scholar
[5] Dehghanian, M. —Park, C.: C*-Ternary 3-homomorphisms on C*-ternary algebras, Results. Math. 66(3) (2014), 87–98.Search in Google Scholar
[6] Dehghanian, M.—Sayyari, Y.—Park, C.: Hadamard homomorphisms and Hadamard derivations on Banach algebras, Miskolc Math. Notes 24(1) (2023), 129–137.Search in Google Scholar
[7] Diaz, J. B.—Margolis, B.: A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Am. Math. Soc. 74 (1968), 305–309.Search in Google Scholar
[8] Haddadi, M. R.—Dehghanian, M.: Existence and convergence theorems for equilibrium problems and fixed point problem, Southeast Asian Bull. Math. 42(4) (2018), 559–568.Search in Google Scholar
[9] Hyers, D. H.: On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222–224.Search in Google Scholar
[10] Hwang, I.—Park, C.: Bihom derivations in Banach algebras, J. Fixed Point Theory Appl. 21 (2019), Art. No. 81.Search in Google Scholar
[11] Lu, G.—Park, C.: Hyers–Ulam stability of general Jensen-type mappings in Banach algebras, Results Math. 66 (2014), 87–98.Search in Google Scholar
[12] Mihet, D.—Radu, V.: On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), 567–572.Search in Google Scholar
[13] Paokanta, S.—Dehghanian, M.—Park, C.—Sayyari, Y.: A system of additive functional equations in complex Banach algebras, Demonstr. Math. 56(1) (2023), Art. ID 20220165.Search in Google Scholar
[14] Park, C.: An additive (α, β)-functional equation and linear mappings in Banach spaces, J. Fixed Point Theory Appl. 18 (2016), 495–504.Search in Google Scholar
[15] Park, C.: Derivation-homomorphism functional inequality, J. Math. Inequal. 15(1) (2021), 95–105.Search in Google Scholar
[16] Park, C.—Rassias, J. M.—Bodaghi, A.—Kim, S.: Approximate homomorphisms from ternary semigroups to modular spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), 2175–2188.Search in Google Scholar
[17] Sayyari, Y.—Dehghanian, M.—Nasiri, Sh.: Solution of some irregular functional equations and their stability, J. Lin. Topol. Alg. 11(4) (2022), 271–277.Search in Google Scholar
[18] Sayyari, Y.—Dehghanian, M.—Park, C.: A system of biadditive functional equations in Banach algebras, Appl. Math. Sci. Eng. 31(1) (2023), Art. ID 2176851.Search in Google Scholar
[19] Sayyari, Y.—Dehghanian, M.—Park, C.: Some stabilities of system of differential equations using Laplace transform, J. Appl. Math. Comput. 69 (2023), 3113–3129.Search in Google Scholar
[20] Sayyari, Y.—Dehghanian, M.—Park, C.—Lee, J. R.: Stability of hyper homomorphisms and hyper derivations in complex Banach algebras, AIMS Math. 7(6) (2022), 10700–10710.Search in Google Scholar
[21] Ulam, S. M.: A Collection of the Mathematical Problem, Interscience, New York, 1960.Search in Google Scholar
© 2024 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Prof. RNDr. Gejza Wimmer, DrSc. – 3/4 C?
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- A fixed point technique to the stability of Hadamard 𝔇-hom-der in Banach algebras
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- Variations of star selection principles on hyperspaces
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- Large deviations for some dependent heavy tailed random sequences
- Metric, stratifiable and uniform spaces of G-permutation degree
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Articles in the same Issue
- Prof. RNDr. Gejza Wimmer, DrSc. – 3/4 C?
- On hyper (r, q)-Fibonacci polynomials
- The pointfree version of 𝓒c(X) via the ranges of functions
- On the x-coordinates of Pell equations that are products of two Pell numbers
- Subordination properties and coefficient problems for a novel class of convex functions
- Certain radii problems for 𝓢∗(ψ) and special functions
- On direct and inverse Poletsky inequalities with a tangential dilatation
- Fourth-order nonlinear strongly non-canonical delay differential equations: new oscillation criteria via canonical transform
- Hermite interpolation of type total degree associated with certain spaces of polynomials
- Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem
- A fixed point technique to the stability of Hadamard 𝔇-hom-der in Banach algebras
- Compact subsets of Cλ,u(X)
- Variations of star selection principles on hyperspaces
- On lower density operators
- Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠2t,3
- On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence
- Large deviations for some dependent heavy tailed random sequences
- Metric, stratifiable and uniform spaces of G-permutation degree
- In memory of Paolo