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Investigations on the Hyers-Ulam stability of generalized radical functional equations. (English) Zbl 1441.39029
This is a continuation of the investigation presented by J. Brzdȩk and J. Schwaiger [Aequationes Math. 92, No. 5, 975–991 (2018; Zbl 1397.39016)]. Here the authors prove the Hyers-Ulam stability of some generalized radical functional equations by using a unified approach.
##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges
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##### References:
 [1] Alizadeh, Z.; Ghazanfari, AG, On the stability of a radical cubic functional equation in quasi-$$\beta$$-spaces, J. Fixed Point Theory Appl., 18, 4, 843-853 (2016) · Zbl 1356.41009 [2] Altun, I.; Sola, F.; Simsek, H., Generalized contractions on partial metric spaces, Topol. Appl., 157, 18, 2778-2785 (2010) · Zbl 1207.54052 [3] Harandi, A.A.: Metric-like spaces, partial metric spaces and fixed points. Fixed Point Th. Appl. (2012), Article ID: 204 · Zbl 1398.54064 [4] Boriceanu, M.; Bota, M.; Petruşel, A., Multivalued fractals in $$b$$-metric spaces, Cent. Eur. J. Math., 8, 2, 367-377 (2010) · Zbl 1235.54011 [5] Brzdęk, J., Remarks on solutions to the functional equations of the radical type, Adv. Theory Nonlinear Anal. Appl., 1, 125-135 (2017) · Zbl 1412.39024 [6] Brzdęk, J.; Popa, D.; Raşa, I.; Xu, B., Ulam Stability of Operators, Mathematical Analysis and Its Applications v. 1 (2018), Oxford: Academic Press, Oxford · Zbl 1393.39001 [7] Brzdęk, J.; Schwaiger, J., Remarks on solutions to a generalization of the radical functional equations, Aeq. Math., 92, 975-991 (2018) · Zbl 1397.39016 [8] Bukatin, M.; Kopperman, R.; Matthews, SG; Pajoohesh, S,H, Partial metric spaces, Am. Math. Mon., 116, 708-718 (2009) · Zbl 1229.54037 [9] Czerwik, S., Contraction mappings in $$b$$-metric spaces, Acta Math. Univ. Ostrav., 1, 1, 5-11 (1993) · Zbl 0849.54036 [10] Czerwik, S., Nonlinear set-valued contraction mappings in $$b$$-metric spaces, Atti Sem. Math. Fis. Univ. Modena, 46, 263-276 (1998) · Zbl 0920.47050 [11] Deza, MM; Deza, E., Encyclopedia of Distances (2009), Berlin: Springer, Berlin · Zbl 1167.51001 [12] Ding, Y.; Xu, T-Z, Approximate solution of generalized inhomogeneous radical quadratic functional equations in 2-Banach spaces, J. Ineq. Appl., 31, 13 (2019) [13] Dung, NV; Hang, VTL, The generalized hyperstability of general linear equations in quasi-Banach spaces, J. Math. Anal. Appl., 462, 131-147 (2018) · Zbl 1391.39033 [14] Forti, GL, An existence and stability theorem for a class of functional equations, Stochastica, 4, 1, 23-30 (1980) · Zbl 0436.60044 [15] Forti, GL, Hyers-Ulam stability of functional equations in several variables, Aeq. Math., 50, 1-2, 143-190 (1995) · Zbl 0836.39007 [16] Forti, GL, Continuous increasing weakly bisymmetric groupoids and quasi-groups in $$\mathbb{R}$$, Math. Pannonica, 8, 49-71 (1997) · Zbl 0880.39017 [17] Gǎvruţa, P., A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184, 3, 431-436 (1994) · Zbl 0818.46043 [18] Hejmej, B., Stability of functional equations in dislocated quasi-metric spaces, Ann. Math. Sil., 32, 215-225 (2018) · Zbl 06946314 [19] Karapınar, E.; Erha, IM, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24, 1894-1899 (2011) · Zbl 1229.54056 [20] Khodaei, H.; Eshaghi Gordji, M.; Kim, SS; Cho, YJ, Approximation of radical functional equations related to quadratic and quartic mappings, J. Math. Anal. Appl., 395, 1, 284-297 (2012) · Zbl 1259.39016 [21] Kim, SS; Cho, YJ; Eshaghi Gordji, M., On the generalized Hyers-Ulam-Rassias stability problem of radical functional equations, J. Inequal. Appl., 2012, 13 (2012) · Zbl 1272.30013 [22] Maligranda, L., Aoki, T.: (1910-1989). In: Proceedings of the International Symposium on Banach and Function Spaces II, Kitakyushu, Japan, 2006, Yokohama Publishers, pp. 1-23 (2008) [23] Maligranda, L., A result of Tosio Aoki about a generalization of Hyers-Ulam stability of additive functions—a question of priority, Aeq. Math., 75, 289-296 (2008) · Zbl 1158.39019 [24] Paluszyński, M.; Stempak, K., On quasi-metric and metric spaces, Proc. Am. Math. Soc., 137, 12, 4307-4312 (2009) · Zbl 1191.54022 [25] Rahman, MU; Sarwar, M., Some new fixed point theorems in dislocated quasi-metric spaces, Palest. J. Math., 5, 171-176 (2015) · Zbl 1348.54058 [26] Rassias, JM; Kim, H-M, Generalized Hyers-Ulam stability for general additive functional equations in quasi-$$\beta$$-normed spaces, J. Math. Anal. Appl., 356, 1, 302-309 (2009) · Zbl 1168.39015 [27] Sarwar, M.; Rahman, MU; Ali, G., Some fixed point results in dislocated quasi metric $$(dq$$-metric) spaces, J. Inequal. Appl., 2014, 278 (2014) · Zbl 1332.54217 [28] Schroeder, V., Quasi-metric and metric spaces, Conform. Geom. Dyn., 10, 355-360 (2006) · Zbl 1113.54014
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