×
Dehghanian, Mehdi; Sayyari, Yamin; Donganont, Siriluk; Park, Choonkil

A Pexider system of additive functional equations in Banach algebras. (English) Zbl 1540.39032

J. Inequal. Appl. 2024, Paper No. 27, 9 p. (2024).

MSC:

39B72 Systems of functional equations and inequalities
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges

Keywords:

Hyers-Ulam stability; \(g\)-derivation; additive mapping; fixed point method; system of functional equations
Cite Review PDF
Full Text: DOI
OA License

References:

[1] Mirzavaziri, M.; Moslehian, M. S., Automatic continuity of σ-derivations on \(C^*\)-algebras, Proc. Am. Math. Soc., 134, 3319-3327, 2006 · Zbl 1116.46061 · doi:10.1090/S0002-9939-06-08376-6
[2] Park, C.; Lee, J.; Zhang, X., Additive s-functional inequality and hom-derivations in Banach algebras, J. Fixed Point Theory Appl., 21, 18, 2019 · Zbl 1404.39028 · doi:10.1007/s11784-018-0652-0
[3] Ulam, S. M., A Collection of the Mathematical Problems, 1960, New York: Interscience Publ., New York · Zbl 0086.24101
[4] Hyers, D. H., On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA, 27, 222-224, 1941 · Zbl 0061.26403 · doi:10.1073/pnas.27.4.222
[5] Aoki, T., On the stability of the linear transformation in Banach spaces, J. Math. Soc. Jpn., 2, 64-66, 1950 · Zbl 0040.35501 · doi:10.2969/jmsj/00210064
[6] Rassias, T. M., On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc., 72, 297-300, 1978 · Zbl 0398.47040 · doi:10.1090/S0002-9939-1978-0507327-1
[7] Găvruta, P., A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184, 431-436, 1994 · Zbl 0818.46043 · doi:10.1006/jmaa.1994.1211
[8] Lee, Y.; Jung, S.; Rassias, M. T., On an n-dimensional mixed type additive and quadratic functional equation, Appl. Math. Comput., 228, 13-16, 2014 · Zbl 1364.39023
[9] Lee, Y.; Jung, S.; Rassias, M. T., Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation, J. Math. Inequal., 12, 1, 43-61, 2018 · Zbl 1412.39028 · doi:10.7153/jmi-2018-12-04
[10] Park, C.; Rassias, M. T., Additive functional equations and partial multipliers in \(C^*\)-algebras, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., 113, 3, 2261-2275, 2019 · Zbl 1435.46038 · doi:10.1007/s13398-018-0612-y
[11] Dehghanian, M.; Modarres, S. M.S., Ternary γ-homomorphisms and ternary γ-derivations on ternary semigroups, J. Inequal. Appl., 2012, 2012 · Zbl 1275.39012 · doi:10.1186/1029-242X-2012-34
[12] Dehghanian, M.; Modarres, S. M.S.; Park, C.; Shin, D., \(C^*\)-Ternary 3-derivations on \(C^*\)-ternary algebras, J. Inequal. Appl., 2013, 2013 · Zbl 1286.39011 · doi:10.1186/1029-242X-2013-124
[13] Dehghanian, M.; Park, C., \(C^*\)-Ternary 3-homomorphisms on \(C^*\)-ternary algebras, Results Math., 66, 3, 385-404, 2014
[14] Czerwik, S., Functional Equations and Inequalities in Several Variables, 2002, River Edge: World Scientific, River Edge · Zbl 1011.39019 · doi:10.1142/4875
[15] Jung, S., On the Hyers-Ulam stability of the functional equations that have the quadratic property, J. Math. Anal. Appl., 222, 126-137, 1998 · Zbl 0928.39013 · doi:10.1006/jmaa.1998.5916
[16] Eshaghi Gordji, M.; Hayati, B.; Kamyar, M.; Khodaei, H., On stability and nonstability of systems of functional equations, Quaest. Math., 44, 4, 557-567, 2020 · Zbl 1469.39015 · doi:10.2989/16073606.2020.1728415
[17] EL-Fassi, Iz., Approximate solution of a generalized multi-quadratic type functional equation in Lipschitz space, J. Math. Anal. Appl., 519, 2, 2023 · Zbl 1507.39017 · doi:10.1016/j.jmaa.2022.126840
[18] EL-Fassi, Iz., Generalized hyperstability of a Drygas functional equation on a restricted domain using Brzdȩk’s fixed point theorem, J. Fixed Point Theory Appl., 19, 4, 2529-2540, 2017 · Zbl 1383.39026 · doi:10.1007/s11784-017-0439-8
[19] Dehghanian, M.; Sayyari, Y.; Park, C., Hadamard homomorphisms and Hadamard derivations on Banach algebras, Miskolc Math. Notes, 24, 1, 81-91, 2023 · Zbl 1524.47040 · doi:10.18514/MMN.2023.3928
[20] Sayyari, Y.; Dehghanian, M.; Park, C.; Lee, J., Stability of hyper homomorphisms and hyper derivations in complex Banach algebras, AIMS Math., 7, 6, 10700-10710, 2022 · doi:10.3934/math.2022597
[21] Dutta, H.; Kumar, B. V.S.; Al-Shaqsi, K., Approximation of Jensen type reciprocal mappings via fixed point technique, Miskolc Math. Notes, 23, 2, 607-619, 2022 · Zbl 1513.39062 · doi:10.18514/MMN.2022.3631
[22] Lu, G.; Park, C., Hyers-Ulam stability of general Jensen-type mappings in Banach algebras, Results Math., 66, 87-98, 2014 · Zbl 1314.39036 · doi:10.1007/s00025-014-0383-5
[23] 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, 2, 305-309, 1968 · Zbl 0157.29904 · doi:10.1090/S0002-9904-1968-11933-0
[24] Park, C., Homomorphisms between Poisson \(JC^*\)-algebras, Bull. Braz. Math. Soc., 36, 79-97, 2005 · Zbl 1091.39007 · doi:10.1007/s00574-005-0029-z
[25] Mihet, D.; Radu, V., On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl., 343, 567-572, 2008 · Zbl 1139.39040 · doi:10.1016/j.jmaa.2008.01.100
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.