[1] |
A. M. Alanazi, G. Muhiuddin, K. Tamilvanan, E. N. Alenze, A. Ebaid, K. Loganathan, Fuzzy stability results of finite variable additive functional equation: Direct and fixed point methods, <i>Mathematics</i>, <b>8</b> (2020), 1050. doi: <a href=“http://dx.doi.org/10.3390/math8071050.” target=“_blank”>10.3390/math8071050.</a> |
[2] |
M. Arunkumar, S. Karthikeyan, S. Ramamoorthi, Generalized Ulam-Hyers stability of \(N\)-dimensional cubic functional equation in FNS and RNS: various methods, <i>Middle-East J. Sci. Res., </i> <b>24</b> (2016), 386-404. |
[3] |
H, RNS-approximately nonlinear additive functional equations, J. Math. Extension, 6, 11-20 (2012) · Zbl 1314.39034 |
[4] |
E. Baktash, Y. J. Cho, M. Jalili, R. Saadati, S. M. Vaezpour, On the stability of cubic mappings and quadratic mappings in random normed spaces, <i>J. Inequalities Appl.</i>, (2008), Article ID 902187, 11, doi: <a href=“http://dx.doi.org/10.1155/2008/902187.” target=“_blank”>10.1155/2008/902187.</a> · Zbl 1165.39022 |
[5] |
S. S. Chang, Y. J. Cho, S. M. Kang, <i>Nonlinear operator theory in probabilistic metric spaces</i>, Nova Science Publishers, Inc. New York, (2001). · Zbl 1080.47054 |
[6] |
S, On the stability of the functional equation deriving from quadratic and additive function in random normed spaces via fixed point method, J. Chungcheong Math. Soc., 25, 51-63 (2012) · doi:10.14403/jcms.2012.25.1.051 |
[7] |
K, On the Hyers-Ulam-Rassias stability of a Pexiderized quadratic inequality, Math. Inequal. Appl., 4, 93-118 (2001) · Zbl 0976.39031 |
[8] |
Z. Gajda, On stability of additive mappings, <i>Intern. J. Math. Math. Sci.</i>, <b>14</b> (1991), 431-434. · Zbl 0739.39013 |
[9] |
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 |
[10] |
D, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA., 27, 222-224 (1941) · JFM 67.0424.01 · doi:10.1073/pnas.27.4.222 |
[11] |
Pl. Kannappan, Quadratic functional equation and inner product spaces, <i>Results Math.</i>, <b>27</b> (1995), 368-372. · Zbl 0836.39006 |
[12] |
D, 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 |
[13] |
D. Mihet, The fixed point method for fuzzy stability of the Jensen functional equation, <i>Fuzzy Sets Syst.</i>, doi: <a href=“http://dx.doi.org/10.1016/j.fss.2008.06.014.” target=“_blank”>10.1016/j.fss.2008.06.014.</a> · Zbl 1179.39039 |
[14] |
C, On a functional equation that has the quadratic-multiplicative property, Open Math., 18, 837-845 (2020) · Zbl 1478.39030 · doi:10.1515/math-2020-0032 |
[15] |
C. Park, K. Tamilvanan, B. Noori, M. B. Moghimi, A. Najati, <i>Fuzzy normed spaces and stability of a generalized quadratic functional equation</i>, AIMS Math., <b>5</b> (2020), 7161-7174. · Zbl 1489.39035 |
[16] |
C, Generalized quadratic mappings in several variables, Nonlinear Anal. TMA, 57, 713-722 (2004) · Zbl 1058.39024 · doi:10.1016/j.na.2004.03.013 |
[17] |
J, On approximately of approximatelylinear mappings by linear mappings, J. Funct. Anal. USA., 46, 126-130 (1982) · Zbl 0482.47033 · doi:10.1016/0022-1236(82)90048-9 |
[18] |
M. Rassias, On the stability of the linear mapping in Banach spaces, <i>Proc. Amer. Math. Soc.</i>, <b>72</b> (1978), 297-300. · Zbl 0398.47040 |
[19] |
M. Rassias, On the stability of the quadratic functional equation and its applications, <i>Studia Univ. Babes-Bolyai</i>, (1998), 89-124. · Zbl 1009.39025 |
[20] |
M, Variational problem of some quadratic functionals in complex analysis, J. Math. Anal. Appl., 228, 234-253 (1998) · Zbl 0945.30023 · doi:10.1006/jmaa.1998.6129 |
[21] |
K, On the Ulam stability for the orthogonally general Euler-Lagrange type functional equation, Int. J. Math. Sci. Autumn, 3, 36-47 (2008) |
[22] |
B. Schweizer, A. Sklar, <i>Probabilistic Metric Spaces</i>, Elsevier, North Holand, New York, 1983. · Zbl 0546.60010 |
[23] |
A. N. Sherstnev, On the notion of a random normed space, <i>Dokl. Akad. Nauk SSSR</i>, <b>149</b> (1963), 280-283. · Zbl 0127.34902 |
[24] |
K, Hyers-Ulam stability of a finite variable mixed type quadratic-additive functional equation in quasi-Banach spaces, AIMS Math., 5, 5993-6005 (2020) · Zbl 1489.39036 · doi:10.3934/math.2020383 |
[25] |
K, Ulam stability of a functional equation deriving from quadratic and additive mappings in random normed spaces, AIMS Math., 6, 908 (2020) · Zbl 1487.39035 |
[26] |
S. M. Ulam, <i>Problems in Modern Mathematics</i>, Science Editions, John Wiley and Sons, 1964. · Zbl 0137.24201 |