Solution of some irregular functional equations and their stability
Subject Areas : Functional analysisY. Sayyari 1 , M. Dehghanian 2 , Sh. Nasiri 3
1 - Department of Mathematics, Sirjan University of Technology, P. O. Box 78137-33385, Sirjan, Iran
2 - Department of Mathematics, Sirjan University of Technology, P. O. Box 78137-33385, Sirjan, Iran
3 - Department of Computer Engineering, Sirjan University of Technology P. O. Box 78137-33385, Sirjan, Iran
Keywords:
Abstract :
[1] C. Baak, Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces, Acta Math. Sin. 22 (2006), 1789-1796.
[2] M. Dehghanian, S. M. S. Modarres, Ternary γ-homomorphisms and ternary γ-derivations on ternary semi-groups, J. Inequal. Appl. (2012), 2012:34.
[3] M. Dehghanian, S. M. S. Modarres, C. Park, D. Y. Shin, C∗-Ternary 3-derivations on C∗-ternary algebras, J. Inequal. Appl. (2013), 2013:124.
[4] M. Dehghanian, C. Park, C∗-Ternary 3-homomorphisms on C∗-ternary algebras, Results. Math. 66 (2014), 87-98.
[5] P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436.
[6] Y. Guan, M. Feckan, J. Wang, Periodic solutions and HyersUlam stability of atmospheric Ekman flows, Discrete Contin. Dyn. Syst. 41 (3) (2021), 1157-1176.
[7] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224.
[8] D. H. Hyers, G .Isac, Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Basel, 1998.
[9] G. Isac, Th. M. Rassias, On the Hyers-Ulam stability of ψ-additive mappings, J. Approx. Theory. 72 (1993), 131-137.
[10] A. Najati, J. R. Lee, C. Park, Th. M. Rassias, On the stability of a Cauchy type functional equation, Demonstr. Math. 51 (2018), 323-331.
[11] C. Park, An additive (α,β)-functional equation and linear mappings in Banach spaces, J. Fixed Point Theory Appl. 18 (2016), 495-504.
[12] C. Park, The stability of an additive (ρ1,ρ2) -functional inequality in Banach spaces, J. Math. Inequal. 13 (1) (2019), 95-104.
[13] C. Park, H. Wee, Homomorphisms between Poisson Banach algebras and Poisson brackets, Honam Math. J. 26 (2004), 61-75.
[14] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (2) (1978), 297-300.
[15] Y. Sayyari, M. Dehghanian, C. Park, J. R. Lee, Stability of hyper homomorphisms and hyper derivations in complex Banach algebras, AIMS. 7 (6) (2022), 10700-10710.
[16] S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publication, New York, 1960.