All Title Author
Keywords Abstract

Publish in OALib Journal
ISSN: 2333-9721
APC: Only $99

ViewsDownloads

Outstanding Development of the Quadratic Φ(μ1,μ2)-Functional Inequatities with 2k-Variables in Fuzzy Banach Space

DOI: 10.4236/oalib.1110592, PP. 1-17

Subject Areas: Mathematics

Keywords: Generalized Quadratic Type &Phi,(&mu,1,&mu,2)-Functional Inequality, Generalized Quadratic Type Functional Equations, Fuzzy Banach Space, Fuzzy Normed Vector Spaces

Full-Text   Cite this paper   Add to My Lib

Abstract

In this paper, I work on expanding the Quadratic Φ(μ1,μ2)-function inequalities by relying on the general quadratic functional equation with 2k-variables on the fuzzy Banach space. That’s the main result of this.

Cite this paper

An, L. V. (2023). Outstanding Development of the Quadratic Φ(μ1,μ2)-Functional Inequatities with 2k-Variables in Fuzzy Banach Space. Open Access Library Journal, 10, e592. doi: http://dx.doi.org/10.4236/oalib.1110592.

References

[1]  Ulam, S.M. (1960) A Collection of Mathematical Problems. Volume 8, Interscience Publishers, New York.
[2]  Hyers, D.H. (1941) On the Stability of the Functional Equation. Proceedings of the National Academy of the United States of America, 27, 222-224. https://doi.org/10.1073/pnas.27.4.222
[3]  Aoki, T. (1950) On the Stability of the Linear Transformation in Banach Space. Journal of the Mathematical Society of Japan, 2, 64-66. https://doi.org/10.2969/jmsj/00210064
[4]  Rassias, Th.M. (1978) On the Stability of the Linear Mapping in Banach Spaces. Proceedings of the American Mathematical Society, 72, 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
[5]  Găvrut, P. (1994) A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings. Journal of Mathematical Analysis and Applications, 184, 431-436. https://doi.org/10.1006/jmaa.1994.1211
[6]  Jun, K. and Kim, H. (2002) The Generalized Hyers-Ulam-Rassias Stability of a Cubic Functional Equation. Journal of Mathematical Analysis and Applications, 274, 867-878. https://doi.org/10.1016/S0022-247X(02)00415-8
[7]  Lee, S., Im, S. and Hwang, I. (2005) Quartic Functional Equations. Journal of Mathematical Analysis and Applications, 307, 387-394. https://doi.org/10.1016/j.jmaa.2004.12.062
[8]  Gilányi, A. (2001) Eine zur Parallelogrammgleichung äquivalente Ungleichung. Aequationes Mathematicae, 62, 303-309. https://doi.org/10.1007/PL00000156
[9]  Rätz, J. (2003) On Inequalities Associated with the Jordan-von Neumann Functional Equation. Aequationes Matheaticae, 66, 191-200. https://doi.org/10.1007/s00010-003-2684-8
[10]  Park, C., Cho, Y. and Han, M. (2007) Stability of Functional Inequalities Associated with Jordan-von Neumann Type Additive Functional Equations. Journal of Inequalities and Applications, 2007, Article ID: 041820. https://doi.org/10.1155/2007/41820
[11]  Fechner, W. (2006) Stability of a Functional Inequality Associated with the Jordan-Von Neumann Functional Equation. Aequationes Mathematicae, 71, 149-161. https://doi.org/10.1007/s00010-005-2775-9
[12]  Bag, T. and Samanta, S.K. (2003) Finite Dimensional Fuzzy Normed Linear Spaces. The Journal of Fuzzy Mathematics, 11, 687-705
[13]  Mirmostafaee, A.K. and Moslehian, M.S. (2008) Fuzzy Versions of Hyers-Ulam-Rassias Theorem. Fuzzy Sets and Systems, 159, 720-729. https://doi.org/10.1016/j.fss.2007.09.016
[14]  Mirmostafaee, A.K. and Moslehian, M.S. (2008) Fuzzy Approximately Cubic Mappings. Information Sciences, 178, 3791-3798. https://doi.org/10.1016/j.ins.2008.05.032
[15]  Mirmostafaee, A.K., Mirzavaziri, M. and Moslehian, M.S. (2008) Fuzzy Stability of the Jensen Functional Equation. Fuzzy Sets and Systems, 159, 730-738. https://doi.org/10.1016/j.fss.2007.07.011
[16]  Katsaras, A.K. (1984) Fuzzy Topological Vector Spaces II. Fuzzy Sets and Systems, 12, 143-154. https://doi.org/10.1016/0165-0114(84)90034-4
[17]  Cădariu, L. andRadu, V. (2003) The Fixed Point Alternative and the Stability of Functional Equations. Fixed Point Theory, 4, 91-96.
[18]  Diaz, J. and Margolis, B. (1968) A Fixed Point Theorem of the Alternative for Contractions on a Generalized Complete Metric Space. Bulletin of the American Mathematical Society, 74, 305-309. https://doi.org/10.1090/S0002-9904-1968-11933-0
[19]  Van An, L. (2020) Generalized Hyers-Ulam Type Stability of the Type Functional Equation with 2k-Variable in Non-Archimedean Space. International Journal of Mathematics Trends and Technology, 66, 134-147. https://doi.org/10.14445/22315373/IJMTT-V66I7P518
[20]  An, L.V. (2020) Generalized Hyers-Ulam Type Stability of the Additive Functional Equation Inequalities with 2n-Variables on an Approximate Group and Ring Homomorphism. Asia Mathematika, 4, 161-175.
[21]  An, L.V. (2021) Generalized Hyers-Ulam-Rassias Type Stability of the with 2k-Variable Quadratic Functional Inequalities in Non-Archimedean Banach Spaces and Banach Spaces. Asia Mathematika, 5, 69-83. https://doi.org/10.14445/22315373/IJMTT-V67I9P521
[22]  An, L.V. (2021) Generalized Hyers-Ulam Type Stability of the 2k-Variables Quadratic β-Functional Inequalities and Function in γ-Homogeneous Normed Space. International Journal of Mathematics and Its Applications, 9, 81-93.
[23]  An, L.V. (2023) Generalized Stability of Functional Inequalities with 3k-Variables Associated for Jordan-von Neumann-Type Additive Functional Equation. Open Access Library Journal, 10, e9681.
[24]  Park, C., Najati, A. and Jang, S. (2013) Fixed Points and Fuzzy Stability of an Additive-Quadratic Functional Equation. Journal of Computational Analysis and Applications, 15, 452-462.
[25]  Park, C. and Rassias, Th.M. (2007) Fixed Points and Generalized Hyers-Ulam Stability of Quadratic Functional Equations. Journal of Mathematical Inequalities, 1, 515-528. https://doi.org/10.7153/jmi-01-43
[26]  Radu, V. (2003) The Fixed Point Alternative and the Stability of Functional Equations. Fixed Point Theory, 4, 91-96.
[27]  Chang, I. and Lee, Y. (2013) Additive and Quadratic Type Functional Equation and Its Fuzzy Stability. Results in Mathematics, 63, 717-730. https://doi.org/10.1007/s00025-012-0229-y
[28]  Cheng, S.C. and Mordeson, J.M. (1994) Fuzzy Linear Operators and Fuzzy Normed Linear Spaces. Bulletin of the Calcutta Mathematical Society, 86, 429-436.
[29]  Rassias, T.M. (2000) On the Stability of Functional Equations in Banach Spaces. Journal of Mathematical Analysis and Applications, 251, 264-284. https://doi.org/10.1006/jmaa.2000.7046
[30]  Rassias, Th.M. (1990) Problem 16; 2, Report of the 27th International Symposium on Functional Equations. Aequationes Mathematicae, 39, 292-293, 309.
[31]  Gajda, Z. (1991) On Stability of Additive Mappings. International Journal of Mathematics and Mathematical Sciences, 14, 431-434. https://doi.org/10.1155/S016117129100056X
[32]  Rassias, Th.M. and Semrl, P. (1992) On the Behavior of Mappings Which Do Not Satisfy Hyers-Ulam Stability. Proceedings of the American Mathematical Society, 114, 989-993. https://doi.org/10.1090/S0002-9939-1992-1059634-1
[33]  An, L.V. (2021) Generalized Hyers-Ulam Stability of the Additive Functional Inequalities with 2n-Variables in Non-Archimedean Banach Space. Bulletin of Mathematics and Statistics Research, 9, 67-73.
[34]  An, L.V. (2023) Generalized Stability of Functional Inequalities with 3k-Variables Associated for Jordan-von Neumann-Type Additive Functional Equation. Open Access Library Journal, 10, e9681. https://www.scirp.org/journal/oalibj https://doi.org/10.4236/oalib.1109681
[35]  Lee, J.R., Park, C. and Shin, D.Y. (2014) Additive and Quadratic Functional in Equalities in Non-Archimedean Normed Spaces. International Journal of Mathematical Analysis, 8, 1233-1247. https://www.m-hikari.com https://doi.org/10.12988/ijma.2014.44113
[36]  Rassias, J.M. (1982) On Approximation of Approximately Linear Mappings by Linear Mappings. Journal of Functional Analysis, 46, 126-130. https://doi.org/10.1016/0022-1236(82)90048-9
[37]  Acze’l, J. and Dhombres, J. (1989) Functional Equations in Several Variables, with Applications to Mathematics, Information Theory and to the Natural and Social Sciences. Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge.
[38]  Cadariu, L. and Radu, V. (2003) Fixed Points and the Stability of Jensen’s Functional Equation. JIPAM. Journal of Inequalities in Pure and Applied Mathematics, 4, Article No. 4.
[39]  Chang, I.S., Eshaghi Gordji, M., Khodaei, H. and Kim, H.M. (2013) Nearly Quartic Mappings in β-Homogeneous F-Spaces. Results in Mathematics, 63, Article ID: 529541. https://doi.org/10.1007/s00025-011-0215-9
[40]  Cho, Y.J., Park, C.K. and Saadati, R. (2010) Functional Inequalities in Non-Archimedean Banach Spaces. Applied Mathematics Letters, 23, 1238-1242. https://doi.org/10.1016/j.aml.2010.06.005
[41]  Cholewa, P.W. (1984) Remarks on the Stability of Functional Equations. Aequationes Mathematicae, 27, 76-86. https://doi.org/10.1007/BF02192660
[42]  Ebadian, A., Ghobadipour, N., Rassias, T.M. and Eshaghi Gordji, M. (2011) Functional Inequalities Associated with Cauchy Additive Functional Equation in Non-Archimedean Spaces. Discrete Dynamics in Nature and Society, 2011, Article ID: 929824. https://doi.org/10.1155/2011/929824
[43]  Isac, G. and Rassias, T.M. (1993) On the Hyers-Ulam Stability of Additive Mappings. Journal of Approximation Theory, 72, 131-137. https://doi.org/10.1006/jath.1993.1010
[44]  Lakshmikantham, V., Leela, S. and Devi, J.V. (2009) Theory of Fractional Dynamic Systems. Cambridge Scientific Publishers, Cambridge.
[45]  Lee, S.-B., Bae, J.-H. and Park, W.-G. (2014) On the Stability of an Additive Functional Inequality for the Fixed Point Alternative. Journal of Computational Analysis and Applications, 17, 361-371.
[46]  Lu, G. and Park, C.K. (2011) Hyers-Ulam Stability of Additive Set-Valued Functional Equations. Applied Mathematics Letters, 24, 1312-1316. https://doi.org/10.1016/j.aml.2011.02.024
[47]  Park, C.K., Cho, Y.S. and Han, M.-H. (2007) Functional Inequalities Associated with Jordan-von Neumann-Type Additive Functional Equations. Journal of Inequalities and Applications, 2007, Article ID: 041820. https://doi.org/10.1155/2007/41820
[48]  Rassias, T.M. (2000) Functional Equations and Inequalities. Mathematics and Its Applications. Kluwer Academic Publishers, Dordrecht. https://doi.org/10.1007/978-94-011-4341-7
[49]  Rassias, T.M. (2000) On the Stability of Functional Equations and a Problem of Ulam. Acta Applicandae Mathematicae, 62, 23-130. https://doi.org/10.1023/A:1006499223572
[50]  Rassias, M. (2007) Refined Hyers-Ulam Approximation of Approximately Jensen Type Mappings. Bulletin des Sciences Mathématiques, 131, 89-98. https://doi.org/10.1016/j.bulsci.2006.03.011
[51]  Rassias, M. and Rassias, M.J. (2003) On the Ulam Stability of Jensen and Jensen Type Mappings on Restricted Domains. Journal of Mathematical Analysis and Applications, 281, 516-524. https://doi.org/10.1016/S0022-247X(03)00136-7
[52]  Jun, K.-W. and Lee, Y.-H. (2004) A Generalization of the Hyers-Ulam-Rassias Stability of the Pexiderized Quadratic Equations. Journal of Mathematical Analysis and Applications, 297, 70 86. https://doi.org/10.1016/j.jmaa.2004.04.009
[53]  Gilanyi, A. (2001) Eine zur Parallelogrammgleichung aquivalente Ungleichung. Aequationes Mathematicae, 62, 303-309. https://doi.org/10.1007/PL00000156
[54]  Bahyrycz, A. and Piszczek, M. (2014) Hyers Stability of the Jensen Function Equation. Acta Mathematica Hungarica, 142, 353-365. https://doi.org/10.1007/s10474-013-0347-3
[55]  Schwaiger, J. (2013) A System of Two Inhomogeneous Linear Functional Equations. Acta Mathematica Hungarica, 140, 377-406. https://doi.org/10.1007/s10474-013-0315-y
[56]  Maligranda, L. (2008) Tosio Aoki (1910-1989). In: International Symposium on Banach and Function Spaces (14/09/2006-17/09/2006), Yokohama Publishers, Yokohama, 1-23.
[57]  Najati, A. and Eskandani, G.Z. (2008) Stability of a Mixed Additive and Cubic Functional Equation in Quasi-Banach Spaces. Journal of Mathematical Analysis and Applications, 342, 1318-1331. https://doi.org/10.1016/j.jmaa.2007.12.039
[58]  Gilányi, A. (2002) On a Problem by K. Nikodem. Mathematical Inequalities & Applications, 5, 707-710. https://doi.org/10.7153/mia-05-71
[59]  Fechner, W. (2010) On Some Functional Inequalities Related to the Logarithmic Mean. Acta Mathematica Hungarica, 128, 36-45. https://doi.org/10.1007/s10474-010-9153-3
[60]  Park, C. (2014) Additive β-Functional Inequalities. Journal of Nonlinear Sciences and Applications, 7, 296-310. https://doi.org/10.22436/jnsa.007.05.02
[61]  Van An, L. (2019) Hyers-Ulam Stability of Functional Inequalities with Three Variable in Banach Spaces and non-Archimedean Banach Spaces. International Journal of Mathematical Analysis, 13, 519-537. https://doi.org/10.12988/ijma.2019.9954
[62]  Cho, Y.J., Park, C. and Saadati, R. (2010) Functional in Equalities in Non-Archimedean Normed Spaces. Applied Mathematics Letters, 23, 1238-1242. https://doi.org/10.1016/j.aml.2010.06.005
[63]  Aribou, Y. and Kabbaj, S. (2018) Generalized Functional in Inequalities in Non-Archimedean Normed Spaces. Applied Mathematics Letters, 2, 61-66.
[64]  An, L.V. (2020) Hyers-Ulam Stability Additive β-Functional Inequalities with Three Variable in Non-Archimedean Banach Space and Complex Banach Spaces. International Journal of Mathematical Analysis, 14, 219-239. https://doi.org/10.12988/ijma.2020.91169
[65]  An, L.V. (2023) Establish an Additive (s; t)-Function Inequlities Fixed Point Method and Direct Method with n-Variables Banach Space. IJRDO—Journal of Mathematics, 9, 1-13. https://doi.org/10.53555/m.v9i1.5515

Full-Text


comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133

WeChat 1538708413