Fuzzy controller and stabilizer on random operators
Resumo
In a random operator inequality, by the fuzzy controllers, we stable an approximately additive odd random operator and find an estimation for such random operators and we solve Hyers-Ulam-Rassias stability problem for a random operator inequality.
Downloads
Referências
Katsaras, A. K., Fuzzy topological vector spaces. I. Fuzzy Sets Syst. 6 , no. 1, 85-95, (1981). https://doi.org/10.1016/0165-0114(81)90082-8
H¨ohle, U., Minkowski functionals of L-fuzzy sets. Fuzzy sets: theory and application to policy analysis and information systems 13-24, (1980). https://doi.org/10.1007/978-1-4684-3848-2_2
Kaleva, O.; Seikkala, S., On fuzzy metric spaces. Fuzzy Sets Syst. 12, no. 3, 215-229, (1984). https://doi.org/10.1016/0165-0114(84)90069-1
Morsi, Nehad N., On fuzzy pseudo-normed vector spaces. Fuzzy Sets Syst. 27, no. 3, 351-372, (1988). https://doi.org/10.1016/0165-0114(88)90061-9
Serstnev, A. N., On the notion of a random normed space. Dokl. Akad. Nauk. USSR. 149(2), 280-283, (1963); Soviet Math. 4(2), (1963).
Mustari, D. H., Almost sure convergence in linear spaces of random variables. (Russian) Teor. Verojat. Primen. 15, 351-357, (1970). https://doi.org/10.1137/1115041
Radu, V., Linear operators in random normed spaces. Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 17, 217-220, (1973).
Cheng, S. C.; Mordeson, J. N., Fuzzy linear operators and fuzzy normed linear spaces. Bull. Calcutta Math. Soc. 86, 429-436, (1994).
Rano, G.; Bag, T., Fuzzy normed linear spaces. Int. J. Math. Sci. Comput. 2, 16-19, (2012).
Narayanan, A.; Vijayabalaji, S., Fuzzy n-normed linear space. Int. J. Math. Math. Sci. 24, 3963-3977, (2005). https://doi.org/10.1155/IJMMS.2005.3963
Vijayabalaji, S.; Thillaigovindan, N., Best approximation sets in α-n-normed space corresponding to intuitionistic fuzzy n-normed linear space. Iran. J. Fuzzy Syst. 5, 57-69, (2008).
Efe, H.; Yildiz, C., Some results in fuzzy compact linear operators. J. Comput. Anal. Appl. 12, no. 1-B, 251-262, (2010).
Lu, G.; Xin, J.; Jin, Y.; Park, C., Approximation of general Pexider functional inequalities in fuzzy Banach spaces. J. Nonlinear Sci. Appl. 12, no. 4, 206-216, (2019). https://doi.org/10.22436/jnsa.012.04.02
Savas, E., Some new double sequence spaces defined by Orlicz function in n-normed space. J. Inequal. Appl. Art. ID 592840, 9 pp, (2011). https://doi.org/10.1155/2011/592840
Hazarika, B.; Sava¸s, E., λ-statistical convergence in n-normed spaces. An. S¸tiint¸. Univ. "Ovidius" Constant¸a Ser. Mat. 21, no. 2, 141-153, (2013). https://doi.org/10.2478/auom-2013-0028
Savas, E.; Gurdal, M., Generalized statistically convergent sequences of functions in fuzzy 2-normed spaces. J. Intell. Fuzzy Systems 27, no. 4, 2067-2075, (2014). https://doi.org/10.3233/IFS-141172
Nsdaban, S.; Bınzar, T.; Pater, F., Some fixed point theorems for ϕ-contractive mappings in fuzzy normed linear spaces. J. Nonlinear Sci. Appl. 10, no. 11, 5668-5676, (2017). https://doi.org/10.22436/jnsa.010.11.05
Font, J. J.; Galindo, J.; Macario, S.; Sanchis, M., Mazur-Ulam type theorems for fuzzy normed spaces. J. Nonlinear Sci. Appl. 10, no. 8, 4499-4506, (2017). https://doi.org/10.22436/jnsa.010.08.41
Khan M. S.; Mahendra S. Y., Maniu G., Postolache, M., On (α, p)-convex contraction and asymptotic regularity. J. Math. Comput. Sci. 18, 132-145, (2018). https://doi.org/10.22436/jmcs.018.02.01
Cho, Y. J.; Rassias, Th. M.; Saadati, R., Fuzzy operator theory in mathematical analysis. Springer, Cham, (2018). https://doi.org/10.1007/978-3-319-93501-0
Binzar, T.; Pater, F.; Nadaban, S., On fuzzy normed algebras. J. Nonlinear Sci. Appl. 9, 5488-5496, (2016). https://doi.org/10.22436/jnsa.009.09.16
Bartwal, A.; Dimri, R. C.; Prasad, G., Some fixed point theorems in fuzzy bipolar metric spaces. J. Nonlinear Sci. Appl. 13 , no. 4, 196-204, (2020). https://doi.org/10.22436/jnsa.013.04.04
Abu-Donia, H. M.; Atia, H. A.; Khater, Omnia M. A., Common fixed point theorems in intuitionistic fuzzy metric spaces and intuitionistic (φ, ψ)-contractive mappings. J. Nonlinear Sci. Appl. 13, no. 6, 323-329, (2020). https://doi.org/10.22436/jnsa.013.06.03
Al-Mazrooei, A. E., Ahmad J., Fuzzy fixed point results of generalized almost F-contraction. J Math Comput SCI-JM. 18, 206-215, (2018). https://doi.org/10.22436/jmcs.018.02.08
Pap, E.; Park, C.; Saadati, R., Additive σ-random operator inequality and rhom-derivations in fuzzy Banach algebras. Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 82, 3-14, (2020).
Ahmed, M. A.; Beg, Ismat; Khafagy, S. A.; Nafadi, H. A., Fixed points for a sequence of L-fuzzy mappings in nonArchimedean ordered modified intuitionistic fuzzy metric spaces. J. Nonlinear Sci. Appl. 14 , no. 2, 97-108, (2021). https://doi.org/10.22436/jnsa.014.02.05
Agarwal, R. P.; Saadati, R.; Salamati, A., Approximation of the multiplicatives on random multi-normed space. J. Inequal. Appl. Paper No. 204, 10 pp, (2017). https://doi.org/10.1186/s13660-017-1478-9
Cho, Y. J.; Rassias, Th. M.; Saadati, R., Springer Optimization and Its Applications, 86. Springer, New York, (2013).
El-hady E., Ogrekci S., On Hyers-Ulam-Rassias stability of fractional differential equations with Caputo derivative. J Math Comput SCI-JM. 22, 325-332, (2021). https://doi.org/10.22436/jmcs.022.04.02
El-Ajou A., Taylor's expansion for fractional matrix functions: theory and applications. J Math Comput SCI-JM. 21, 1-17, (2020). https://doi.org/10.22436/jmcs.021.01.01
Khan O., Araci S., Saif M., Fractional calculus formulas for Mathieu-type series and generalized Mittag-Leffler function. J Math Comput SCI-JM. 20, 122-130, (2020). https://doi.org/10.22436/jmcs.020.02.05
Chaharpashlou, R.; Saadati, R.; Atangana, A., Ulam-Hyers-Rassias stability for nonlinear Ψ-Hilfer stochastic fractional differential equation with uncertainty. Adv. Difference Equ. Paper No. 339, 10 pp, (2020). https://doi.org/10.1186/s13662-020-02797-5
Saadati, R.; Pourhadi, E.; Samet, B., On the PC-mild solutions of abstract fractional evolution equations with noninstantaneous impulses via the measure of noncompactness. Bound. Value Probl. Paper No. 19, 23 pp, (2019). https://doi.org/10.1186/s13661-019-1137-9
Youssef, M. I., Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function. J. Nonlinear Sci. Appl. 13, 293-302, (2020). https://doi.org/10.22436/jnsa.013.05.06
El-Sayed, A. M. A.; Al-Issa, Sh. M., Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach. J. Nonlinear Sci. Appl. 13, 180-186, (2020). https://doi.org/10.22436/jnsa.013.04.02
Sene, N., Global asymptotic stability of the fractional differential equations. J. Nonlinear Sci. Appl. 13, 171-175, (2020). https://doi.org/10.22436/jnsa.013.03.06
Sene, N., Stability analysis of the generalized fractional differential equations with and without exogenous inputs. J. Nonlinear Sci. Appl. 12, 562-572, (2019). https://doi.org/10.22436/jnsa.012.09.01
Ahmed H. M., El-Borai M. M., El-Owaidy H. M., Ghanem A. S., Null controllability of fractional stochastic delay integro-differential equations. J Math Comput SCI-JM. 19, 143-150, (2019). https://doi.org/10.22436/jmcs.019.03.01
El-Moneam, M. A.; Ibrahim, Tarek F.; Elamody, S., Stability of a fractional difference equation of high order. J. Nonlinear Sci. Appl. 12, 65-74, (2019). https://doi.org/10.22436/jnsa.012.02.01
Sene N., Exponential form for Lyapunov function and stability analysis of the fractional differential equations. J Math Comput SCI-JM. 18, 388-397, (2018). https://doi.org/10.22436/jmcs.018.04.01
Agarwal R. P., Hristova S., O'Regan D., Lyapunov functions to Caputo reaction-diffusion fractional neural networks with time-varying delays. J Math Comput SCI-JM. 18, 328-345, (2018). https://doi.org/10.22436/jmcs.018.03.08
Cadariu, L.; Radu, V., Fixed points and the stability of Jensen's functional equation. JIPAM. J. Inequal. Pure Appl. Math. 4, Article 4, 7 pp, (2003).
Diaz, J. B.; Margolis, B., A fixed point theorem of the alternative, for contractions on a generalized complete metric space. Bull. Amer. Math. Soc. 74, 305-309, (1968). https://doi.org/10.1090/S0002-9904-1968-11933-0
An, J. S., On an additive functional inequality in normed modules over a C-algebra. J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 15, 393-400, (2008).
Cho, Y. J.; Saadati, R.; Yang, Y.-O.; Kenari, H. M., A fixed point technique for approximate a functional inequality in normed modules over C-algebras. Filomat 30, 1691-1696, (2016). https://doi.org/10.2298/FIL1607691C
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
