zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stability of Cauchy-Jensen type functional equation in generalized fuzzy normed spaces. (English) Zbl 1232.46068
Summary: We establish some stability results concerning the Cauchy-Jensen functional equation in generalized fuzzy normed spaces. The results of the present paper improve and extend some recent results.
MSC:
39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
46S40Fuzzy functional analysis
46S10Functional analysis over fields (not , , or quaternions)
References:
[1]Zadeh, L. A.: Fuzzy sets, inform. Control, Fuzzy sets, inform. Control 8, 338-353 (1965) · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[2]Bag, T.; Samanta, S. K.: Finite dimensional fuzzy normed linear spaces, J. fuzzy math. 11, 687-705 (2003) · Zbl 1045.46048
[3]Bag, T.; Samanta, S. K.: Fuzzy bounded linear operators, Fuzzy sets and systems 151, 513-547 (2005) · Zbl 1077.46059 · doi:10.1016/j.fss.2004.05.004
[4]Barros, L. C.; Bassanezi, R. C.; Tonelli, P. A.: Fuzzy modelling in population dynamics, Ecol. model. 128, 27-33 (2000)
[5]Chang, S. S.; Cho, Y. J.; Wang, F.: On the existence and the uniqueness problem of solutions for set-valued and single-valued nonlinear operator equations in probabilistic normed spaces, Int. J. Math. math. Sci. 17, 389-396 (1994) · Zbl 0801.47043 · doi:10.1155/S0161171294000530
[6]Cho, Y. J.; Huang, H. J.; Kang, S. M.: Nonlinear equations for fuzzy mappings in probabilistic normed spaces, Fuzzy sets and systems 110, 115-122 (2000) · Zbl 0949.47059 · doi:10.1016/S0165-0114(98)00009-8
[7]Fang, J. X.: On I-topology generated by fuzzy norm, Fuzzy sets and systems 157, 2739-2750 (2006) · Zbl 1110.46052 · doi:10.1016/j.fss.2006.03.024
[8]Fradkov, A. L.; Evans, R. J.: Control of chaos: methods and applications in engineering, Chaos solitons fractals 29, 33-56 (2005)
[9]George, A.; Veeramani, P.: On some result in fuzzy metric space, Fuzzy sets and systems 64, 395-399 (1994) · Zbl 0843.54014 · doi:10.1016/0165-0114(94)90162-7
[10]Gregori, V.; Romaguera, S.: Characterizing completable fuzzy metric spaces, Fuzzy sets and systems 144, 411-420 (2004) · Zbl 1057.54010 · doi:10.1016/S0165-0114(03)00161-1
[11]Giles, R.: A computer program for fuzzy reasoning, Fuzzy sets and systems 4, 221-234 (1980) · Zbl 0445.03007 · doi:10.1016/0165-0114(80)90012-3
[12]Hong, L.; Sun, J. Q.: Bifurcations of fuzzy nonlinear dynamical systems, Commun. nonlinear sci. Numer. simul. 1, 1-12 (2006) · Zbl 1078.37049 · doi:10.1016/j.cnsns.2004.11.001
[13]Madore, J.: Fuzzy physics, Ann. phys. 219, 187-198 (1992)
[14]Miheţ, D.: On set-valued nonlinear equations in Menger probabilistic normed spaces, Fuzzy sets and systems 158, 1823-1831 (2007) · Zbl 1116.47062 · doi:10.1016/j.fss.2007.01.007
[15]Saadati, R.: On the L-fuzzy topological spaces, Chaos solitons fractals 37, 1419-1426 (2008) · Zbl 1142.54318 · doi:10.1016/j.chaos.2006.10.033
[16]Saadati, R.; Vaezpour, S. M.; Cho, Y. J.: Quicksort algorithm: application of a fixed point theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words, J. comput. Appl. math. 228, No. 1, 219-225 (2009) · Zbl 1189.68040 · doi:10.1016/j.cam.2008.09.013
[17]Saadati, R.; Park, J. H.: On the intuitionistic fuzzy topological spaces, Chaos, solitons fractals 27, 331-344 (2006) · Zbl 1083.54514 · doi:10.1016/j.chaos.2005.03.019
[18]Ulam, S. M.: Problems in modern mathematics, (1964)
[19]Hyers, D. H.: On the stability of the linear functional equation, Proc. natl. Acad. sci. 27, 222-224 (1941) · Zbl 0061.26403 · doi:10.1073/pnas.27.4.222
[20]Aoki, T.: On the stability of the linear transformation in Banach spaces, J. math. Soc. Japan 2, 64-66 (1950) · Zbl 0040.35501 · doi:10.2969/jmsj/00210064
[21]Rassias, Th.M.: On the stability of the linear mapping in Banach spaces, Proc. amer. Math. soc. 72, 297-300 (1978) · Zbl 0398.47040 · doi:10.2307/2042795
[22]Rassias, J. M.: On approximation of approximately linear mappings by linear mappings, J. funct. Anal. 46, 126-130 (1982) · Zbl 0482.47033 · doi:10.1016/0022-1236(82)90048-9
[23]Forti, G. L.: The stability of homomorphisms and amenability, with applications to functional equations, Abh. math. Sem. univ. Hamburg 57, 215-226 (1987) · Zbl 0619.39012 · doi:10.1007/BF02941612
[24]Gavruta, 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
[25]Cho, Y. J.; Park, C.; Saadati, R.: Functional inequalities in non-Archimedean Banach spaces, Appl. math. Lett. 10, 1238-1242 (2010) · Zbl 1203.39015 · doi:10.1016/j.aml.2010.06.005
[26]Czerwik, S.: On the stability of the quadratic mapping in normed spaces, Abh. math. Sem. univ. Hamburg 62, 59-64 (1992) · Zbl 0779.39003 · doi:10.1007/BF02941618
[27]Gordji, M. Eshaghi: Nearly ring homomorphisms and nearly ring derivations on non-Archimedean Banach algebras, ABS appl. Anal., 12 pages (2010) · Zbl 1218.46050 · doi:10.1155/2010/393247
[28]Gordji, M. Eshaghi; Khodaei, H.: Stability of functional equations, (2010)
[29]Gordji, M. Eshaghi; Khodaei, H.: Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi-Banach spaces, Nonlinear anal.-TMA 71, 5629-5643 (2009) · Zbl 1179.39034 · doi:10.1016/j.na.2009.04.052
[30]Gordji, M. Eshaghi; Savadkouhi, M. B.: Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces, Appl. math. Lett. 23, 1198-1202 (2010) · Zbl 1204.39028 · doi:10.1016/j.aml.2010.05.011
[31]Jung, S. -M.: Hyers–Ulam–rassias stability of functional equations in mathematical analysis, (2001) · Zbl 0980.39024
[32]Hyers, D. H.; Isac, G.; Rassias, Th.M.: Stability of functional equations in several variables, (1998)
[33]Mirmostafaee, A. K.: Stability of quartic mappings in non-Archimedean normed spaces, Kyungpook math. J. 49, No. 2, 289-297 (2009) · Zbl 1179.39040 · doi:http://kmj.knu.ac.kr/xe/?mid=articles&page=1&category=1362&document_srl=1659
[34]Rassias, J. M.: Alternative contraction principle and alternative Jensen and Jensen type mappings, Int. J. Appl. math. Stat. 2, 92-101 (2005)
[35]Rassias, J. M.: Refined Hyers–Ulam approximation of approximately Jensen type mappings, Bull. sci. Math. 131, 89-98 (2007) · Zbl 1112.39025 · doi:10.1016/j.bulsci.2006.03.011
[36]Rassias, J. M.: Solution of a problem of Ulam, J. approx. Theory 57, 268-273 (1989) · Zbl 0672.41027 · doi:10.1016/0021-9045(89)90041-5
[37]Rassias, Th.M.: On the stability of functional equations and a problem of Ulam, Acta appl. Math. 62, 23-130 (2000) · Zbl 0981.39014 · doi:10.1023/A:1006499223572
[38]Th.M. Rassias, Problem 16; 2, in: Report of the 27th International Symp. on Functional Equations, in: Aequationes Math., vol. 39, 1990, pp. 292–293.
[39]Rassias, Th.M.; Šemrl, P.: On the Hyers–Ulam stability of linear mappings, J. math. Anal. appl. 173, 325-338 (1993) · Zbl 0789.46037 · doi:10.1006/jmaa.1993.1070
[40]Gordji, M. Eshaghi; Khodaei, H.: The fixed point method for fuzzy approximation of a functional equation associated with inner product spaces, Disc. dyn. Nature. soc., 15 pages (2010) · Zbl 1221.39036 · doi:10.1155/2010/140767
[41]Miheţ, D.: The fixed point method for fuzzy stability of the Jensen functional equation, Fuzzy sets and systems 160, 1663-1667 (2009) · Zbl 1179.39039 · doi:10.1016/j.fss.2008.06.014
[42]Miheţ, D.: The stability of the additive Cauchy functional equation in non-Archimedean fuzzy normed spaces, Fuzzy sets syst. 161, 2206-2212 (2010) · Zbl 1206.46066 · doi:10.1016/j.fss.2010.02.010
[43]Miheţ, D.; Radu, V.: 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
[44]D. Miheţ, R. Saadati, S.M. Vaezpour, The stability of the quartic functional equation in random normed spaces, Acta Appl. Math., doi:10.1007/s10440–009–9476–7.
[45]Mirmostafaee, A. K.; Mirzavaziri, M.; Moslehian, M. S.: Fuzzy stability of the Jensen functional equation, Fuzzy sets and systems 159, 730-738 (2008) · Zbl 1179.46060 · doi:10.1016/j.fss.2007.07.011
[46]Mirmostafaee, A. K.; Moslehian, M. S.: Fuzzy versions of Hyers–Ulam–rassias theorem, Fuzzy sets and systems 159, 720-729 (2008) · Zbl 1178.46075 · doi:10.1016/j.fss.2007.09.016
[47]Mirmostafaee, A. K.; Moslehian, M. S.: Stability of additive mappings in non-Archimedean fuzzy normed spaces, Fuzzy sets and systems 160, 1643-1652 (2009) · Zbl 1187.46068 · doi:10.1016/j.fss.2008.10.011
[48]Park, C.: Fuzzy stability of a functional equation associated with inner product spaces, Fuzzy sets and systems 160, 1632-1642 (2009) · Zbl 1182.39023 · doi:10.1016/j.fss.2008.11.027
[49]Mursaleen, M.; Mohiuddine, S. A.: On stability of a cubic functional equation in intuitionistic fuzzy normed spaces, Chaos solitons fractals 42, No. 5, 2997-3005 (2009) · Zbl 1198.39035 · doi:10.1016/j.chaos.2009.04.041
[50]Mohiuddine, S. A.: Stability of Jensen functional equation in intuitionistic fuzzy normed space, Chaos solitons fractals 42, No. 5, 2989-2996 (2009) · Zbl 1198.39034 · doi:10.1016/j.chaos.2009.04.040
[51]Saadati, R.; Cho, Y. J.; Vahidi, J.: The stability of the quartic functional equation in various spaces, Comput. math. Appl. 60, 1994-2002 (2010) · Zbl 1205.39029 · doi:10.1016/j.camwa.2010.07.034
[52]Saadati, R.; Park, C.: Non–Archimedean L-fuzzy normed spaces and stability of functional equations, Comput. math. Appl. 60, 2488-2496 (2010) · Zbl 1205.39023 · doi:10.1016/j.camwa.2010.08.055
[53]Mohiuddine, S. A.; Sevli, H.: Stability of pexiderized quadratic functional equation in intuitionistic fuzzy normed space, J. comput. Appl. math. 235, 2137-2146 (2011) · Zbl 1222.39022 · doi:10.1016/j.cam.2010.10.010
[54]Baak, C.: Cauchy–rassias stability of Cauchy–Jensen additive mappings in Banach spaces, Acta math. Sin. (Engl. Ser.) 22, No. 6, 1789-1796 (2006) · Zbl 1118.39012 · doi:10.1007/s10114-005-0697-z
[55]Jun, K. -W.; Kim, H. -M.; Rassias, J. M.: Extended Hyers–Ulam stability for Cauchy–Jensen mappings, J. diference equ. Appl. 13, No. 12, 1139-1153 (2007) · Zbl 1135.39013 · doi:10.1080/10236190701464590
[56]Najati, A.; Ranjbari, A.: Stability of homomorphisms for a 3D Cauchy–Jensen type functional equation on C*-ternary algebras, J. math. Anal. appl. 341, 62-79 (2008) · Zbl 1147.39010 · doi:10.1016/j.jmaa.2007.09.025
[57]Park, C.: Fixed points and Hyers–Ulam–rassias stability of Cauchy–Jensen functional equations in Banach algebras, Fixed. point. Theory. appl., 15 pages (2007) · Zbl 1167.39018 · doi:10.1155/2007/50175
[58]Park, C.; Rassias, J. M.: Stability of the Jensen–type functional equation in C*-algebras: a fixed point approach, ABS appl. Anal., 17 pages (2009)
[59]Hensel, K.: Über eine neue begründung der theorie der algebraischen zahlen, Jahresber deutsch. Math. verein 6, 83-88 (1899) · Zbl 30.0096.03
[60]Vladimirov, V. S.; Volovich, I. V.; Zelenov, E. I.: P-adic analysis and mathematical physics, (1994) · Zbl 0864.46048
[61]Gouvêa, F. Q.: P-adic numbers, (1997)
[62]Khrennikov, A.: P-adic valued distributions in mathematical physics, (1994)
[63]Khrennikov, A.: Non-Archimedean analysis: quantum paradoxes, dynamical syst.ems and biological models, (1997)
[64]Goleţ, I.: On generalized fuzzy normed spaces and coincidence point theorems, Fuzzy sets and systems 161, 1138-1144 (2010) · Zbl 1228.47073 · doi:10.1016/j.fss.2009.10.004
[65]Hadžić, O.; Pap, E.; Budinčević, M.: Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces, Kybernetika 38, No. 3, 363-381 (2002)
[66]Huang, N.; Lan, H.: A couple of nonlinear equations with fuzzy mappings in fuzzy normed spaces, Fuzzy sets and systems 152, 209-222 (2005) · Zbl 1101.47060 · doi:10.1016/j.fss.2004.11.010
[67]Goleţ, I.: On fuzzy normed spaces, Southeast asian bull. Math. 31, 1-10 (2007)
[68]Goleţ, I.: Approximations theorems in probabilistic normed spaces, Novi sad J. Math. 38, No. 3, 73-79 (2008) · Zbl 1224.54071
[69]Goleţ, I.; Goleţ, I.: Approximation of fuzzy normed space valued functions, AIP conf., proc. 936, 244-247 (2007) · Zbl 1152.26338 · doi:10.1063/1.2790120
[70]Goleţ, I.: Some remarks on functions with values in probabilistic normed spaces, Math. slovaca 57, 259-270 (2007) · Zbl 1150.54030 · doi:10.2478/s12175-007-0021-8
[71]Goleţ, I.: On generalized fuzzy normed spaces, Int. math. Forum 4, 1237-1242 (2009) · Zbl 1196.46058 · doi:http://www.m-hikari.com/imf-password2009/25-28-2009/index.html
[72]Schweizer, B.; Sklar, A.: Probabilistic metric spaces, (1983)