A system of additive functional equations in complex Banach algebras

• Autorzy: Paokanta Siriluk , Dehghanian Mehdi , Park Choonkil , Sayyari Yamin

Identyfikatory

DOI

10.1515/dema-2022-0165

• Języki publikacji: EN

Abstrakty

EN

In this article, we solve the system of additive functional equations: [formula] and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of ƒ-hom-ders in Banach algebras.

Słowa kluczowe

EN

additive mapping; f-hom-der; fixed point method; Hyers-Ulam stability; system of additive functional equations

PL

odwzorowania addytywne; metoda punktu stałego; stabilność Hyersa-Ulama

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220165
• Opis fizyczny: Bibliogr. 38 poz.

Twórcy

autor

Paokanta Siriluk

• School of Science, University of Phayao, Phayao 56000, Thailand
• Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

autor

Dehghanian Mehdi

• Department of Mathematics, Sirjan University of Technology, Sirjan, Iran

autor

Park Choonkil

• Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

autor

Sayyari Yamin

• Department of Mathematics, Sirjan University of Technology, Sirjan, Iran

Bibliografia

• [1] M. Mirzavaziri and M. S. Moslehian, Automatic continuity of σ-derivations on ∗C -algebras, Proc. Am. Math. Soc. 134 (2006), no. 11, 3319–3327.
• [2] C. Park, J. Lee, and X. Zhang, Additive s-functional inequality and hom-derivations in Banach algebras, J. Fixed Point Theory Appl. 21 (2019), Paper No. 18, DOI: https://doi.org/10.1007/s11784-018-0652-0.
• [3] M. Dehghanian, C. Park, and Y. Sayyari, On the stability of hom-der on Banach algebras (preprint).
• [4] A. Kheawborisuk, S. Paokanta, and J. Senasukh, Ulam stability of hom-ders in fuzzy Banach algebars, C. Park, AIMS Math. 7 (2022), no. 9, 16556–16568, DOI: https://doi.org/10.3934/math.2022907.
• [5] S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publications, New York, 1960.
• [6] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222–224.
• [7] M. Dehghanian and S. M. S. Modarres, Ternary γ-homomorphisms and ternary γ-derivations on ternary semigroups, J. Inequal. Appl. 2012 (2012), Paper No. 34, DOI: https://doi.org/10.1186/1029-242X-2012-34.
• [8] M. Dehghanian, S. M. S. Modarres, C. Park, and D. Shin, ∗C -Ternary 3-derivations on ∗C -ternary algebras, J. Inequal. Appl. 2013 (2013), Paper No. 124, DOI: https://doi.org/10.1186/1029-242X-2013-124.
• [9] M. Dehghanian and C. Park, ∗C -Ternary 3-homomorphisms on ∗C -ternary algebras, Results Math. 66 (2014), 385–404, DOI: https://doi.org/10.1007/s00025-014-0383-5.
• [10] M. Dehghanian, Y. Sayyari, and C. Park, Hadamard homomorphisms and Hadamard derivations on Banach algebras, Miskolc Math. Notes (in press).
• [11] C. Park, J. M. Rassias, A. Bodaghi, and S. Kim, Approximate homomorphisms from ternary semigroups to modular spaces, Rev. R. Acad. Cienc. Exactas Fiiis. Nat. Ser. A Mat. RACSAM 113 (2019), no. 3, 2175–2188, DOI: https://doi.org/10.1007/s13398-018-0608-7.
• [12] C. Park, K. Tamilvanan, G. Balasubramanian, B. Noori, and A. Najati, On a functional equation that has the quadratic-multiplicative property, Open Math. 18 (2020), 837–845, DOI: https://doi.org/10.1515/math-2020-0032.
• [13] A. Thanyacharoen and W. Sintunavarat, The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimdean spaces, Demonstr. Math. 53 (2020), 174–192, DOI: https://doi.org/10.1515/dema-2020-0009.
• [14] A. Thanyacharoen and W. Sintunavarat, On new stability results for composite functional equations in quasi-β-normed spaces, Demonstr. Math. 54 (2021), 68–84, DOI: https://doi.org/10.1515/dema-2021-0002.
• [15] Y. Sayyari, M. Dehghanian, C. Park, and J. Lee, Stability of hyper homomorphisms and hyper derivations in complex Banach algebras, AIMS Math. 7 (2022), no. 6, 10700–10710, DOI: https://doi.org/10.3934/math.2022597.
• [16] I. Hwang and C. Park, Bihom derivations in Banach algebras, J. Fixed Point Theory Appl. 21 (2019), no. 3, Paper No. 81, DOI: https://doi.org/10.1007/s11784-019-0722-x.
• [17] G. Lu and C. Park, Hyers-Ulam stability of general Jensen-type mappings in Banach algebras, Results Math. 66 (2014), 87–98, DOI: https://doi.org/10.1007/s00025-014-0365-7.
• [18] C. Park, An additive (α β, )-functional equation and linear mappings in Banach spaces, J. Fixed Point Theory Appl. 18 (2016), 495–504, DOI: https://doi.org/10.1007/s11784-016-0283-2.
• [19] C. Park, The stability of an additive ( )ρ ρ,1 2 -functional inequality in Banach spaces, J. Math. Inequal. 13 (2019), 95–104, DOI: https://doi.org/10.7153/jmi-2019-13-07.
• [20] J. Brzdȩk, L. Cădariu, and K. Ciepliński, Fixed point theory and the Ulam stability, J. Funct. Spaces 2014 (2014), Article ID 829419, DOI: https://doi.org/10.1155/2014/829419.
• [21] J. Brzdȩk, E. Karapinar, and A. Petruşel, A fixed point theorem and the Ulam stability in generalized dq-metric spaces, J. Math. Anal. Appl. 467 (2018), no. 1, 501–520, DOI: https://doi.org/10.1016/j.jmaa.2018.07.022.
• [22] D. Popa, G. Pugna, and I. Rasa, On Ulam stability of the second order linear differential equation, Adv. Theory Nonlinear Anal. Appl. 2 (2018), no. 2, 106–112.
• [23] A. Salim, M. Benchohra, E. Karapinar, and J. E. Lazreg, Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations, Adv. Difference Equations 2020 (2020), Paper No. 601, DOI: https://doi.org/10.1186/s13662-020-03063-4.
• [24] A. Lachouri and A. Ardjouni, The existence and Ulam-Hyers stability results for generalized Hilfer fractional integro-differential equations with nonlocal integral boundary conditions, Adv. Theory Nonlinear Anal. Appl. 6 (2022), no. 1, 101–117.
• [25] H. Mohamed, Sequential fractional pantograph differential equations with nonlocal boundary conditions: Uniqueness and Ulam-Hyers-Rassias stability, Results Nonlinear Anal. 5 (2022), no. 1, 29–41, DOI: https://doi.org/10.53006/rna.928654.
• [26] R. Atmania, Existence and stability results for a nonlinear implicit fractional differential equation with a discrete delay, Adv. Theory Nonlinear Anal. Appl. 6 (2022), no. 2, 246–257.
• [27] E. Karapinar, H. D. Binh, N. H. Luc, and N. H. Can, On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems, Adv. Difference Equations 2021 (2021), Paper No. 70, DOI: https://doi.org/10.1186/s13662-021-03232-z.
• [28] J. E. Lazreg, S. Abbas, M. Benchohra, and E. Karapinar, Impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces, Open Math. 19 (2021), 363–372, DOI: https://doi.org/10.1515/math-2021-0040.
• [29] R. S. Adigüzel, U. Aksoy, E. Karapinar, and I. M. Erhan, On the solution of a boundary value problem associated with a fractional differential equation, Math. Methods Appl. Sci. (in press), DOI: https://doi.org/10.1002/mma.6652.
• [30] R. S. Adigüzel, U. Aksoy, E. Karapinar, and I. M. Erhan, Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115 (2021), Paper No. 155, DOI: https://doi.org/10.1007/s13398-021-01095-3.
• [31] R. S. Adigüzel, U. Aksoy, E. Karapinar, and I. M. Erhan, On the solutions of fractional differential equations via Geraghty type hybrid contractions, Appl. Comput. Math. 20 (2021), 313–333.
• [32] H. Afshari and E. Karapinar, A solution of the fractional differential equations in the setting of b-metric space, Carpathian Math. Publ. 13 (2021), 764–774, DOI: https://doi.org/10.15330/cmp.13.3.764-774.
• [33] H. Afshari, H. Shojaat, and M. S. Moradi, Existence of the positive solutions for a tripled system of fractional differential equations via integral boundary conditions, Results Nonlinear Anal. 4 (2021), Article ID 186193, DOI: https://doi.org/10.53006/rna.938851.
• [34] M. Asadi, B. Moeini, A. Mukheimer, and H. Aydi, Complex valued M-metric spaces and related fixed point results via complex C-class functions, J. Inequal. Spec. Funct. 10 (2019), no. 1, 101–110.
• [35] B. Moeini, M. Asadi, H. Aydi, and M. S. Noorani, ∗C -Algebra-valued M-metric spaces and some related fixed point results, Ital. J. Pure Appl. Math. 41 (2019), 708–723.
• [36] J. B. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Am. Math. Soc. 74 (1968), 305–309.
• [37] D. Mihet and V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), no. 1, 567–572, DOI: https://doi.org/10.1016/j.jmaa.2008.01.100.
• [38] C. Park, Homomorphisms between Poisson JC∗ -algebras, Bull. Braz. Math. Soc. 36 (2005), 79–97, DOI: https://doi.org/10.1007/s00574-005-0029-z.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).