Stability of a Mixed Type Functional Equation on Multi-Banach Spaces: A Fixed Point Approach
Using fixed point methods, we prove the Hyers-Ulam-Rassias stability of a mixed type functional equation on multi-Banach spaces.
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| Vydáno v: | Fixed point theory and applications (Hindawi Publishing Corporation) Ročník 2010; číslo 1; s. 283827 |
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01.01.2010
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| Abstract | Using fixed point methods, we prove the Hyers-Ulam-Rassias stability of a mixed type functional equation on multi-Banach spaces. |
|---|---|
| AbstractList | Using fixed point methods, we prove the Hyers-Ulam-Rassias stability of a mixed type functional equation on multi-Banach spaces. |
| ArticleNumber | 283827 |
| Author | Wang, Liguang Liu, Bo Bai, Ran |
| Author_xml | – sequence: 1 givenname: Liguang surname: Wang fullname: Wang, Liguang email: wangliguang0510@163.com organization: School of Mathematical Sciences, Qufu Normal University – sequence: 2 givenname: Bo surname: Liu fullname: Liu, Bo organization: School of Mathematical Sciences, Qufu Normal University – sequence: 3 givenname: Ran surname: Bai fullname: Bai, Ran organization: School of Mathematical Sciences, Qufu Normal University |
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| Copyright | LiguangWang et al. 2010. This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| References | Dales HG, Polyakov ME: Multi-normed spaces and multi-Banach algebras. preprint AokiTOn the stability of the linear transformation in Banach spacesJournal of the Mathematical Society of Japan1950264664058010.2969/jmsj/002100640040.35501 GavrutaPOn a problem of G. Isac and Th. M. Rassias concerning the stability of mappingsJournal of Mathematical Analysis and Applications20012612543553185305510.1006/jmaa.2001.75390993.47002 DalesHGMoslehianMSStability of mappings on multi-normed spacesGlasgow Mathematical Journal2007492321332234726310.1017/S00170895070035521125.39023 RassiasThMOn the stability of the linear mapping in Banach spacesProceedings of the American Mathematical Society197872229730050732710.1090/S0002-9939-1978-0507327-10398.47040 GavrutaPOn the Hyers-Ulam-Rassias stability of the quadratic mappingsNonlinear Functional Analysis and Applications20049341542821011891066.39029 CadariuLRaduVOn the stability of the Cauchy functional equation: a fixed point approachIteration Theory (ECIT '02), Die Grazer Mathematischen Berichte2004Graz, AustriaKarl-Franzens-Universitaet Graz4352 GavrutaPAn answer to a question of Th. M. Rassias and J. Tabor on mixed stability of mappingsBuletinul ŞtiinŞific al Universităţii "Politehnica" din Timişoara. Seria Matematică-Fizică199742(56)11616659920983.39012 HyersDHOn the stability of the linear functional equationProceedings of the National Academy of Sciences of the United States of America194127222224407610.1073/pnas.27.4.2220061.26403 GavrutaLGavrutaPOn a problem of John M. Rassias concerning the stability in Ulam sense of Euler-Lagrange equationFunctional Equations, Difference Inequalities and Ulam Stability Notions20104753Nova Sciences DiazJBMargolisBA fixed point theorem of the alternative, for contractions on a generalized complete metric spaceBulletin of the American Mathematical Society19687430530922026710.1090/S0002-9904-1968-11933-00157.29904 GavrutaPHossuMPopescuDCăprăuCOn the stability of mappings and an answer to a problem of Th. M. RassiasAnnales Mathématiques Blaise Pascal199522556010.5802/ambp.4713718920853.46036 GajdaZOn stability of additive mappingsInternational Journal of Mathematics and Mathematical Sciences1991143431434111003610.1155/S016117129100056X0739.39013 Eshaghi-Gordji M, Kaboli-Gharetapeh S, Moslehian MS, Zolfaghari S: Stability of a mixed type additive, quadratic, cubic and quartic functional equation. In Nonlinear Analysis and Variational Problems, Springer Optimization and Its Applications, 35. Edited by: Pardalos PM, Rassias ThM, Khan AA. Springer, Berlin, Germany; 2009:65–80. ParkCAnJSStability of the Cauchy-Jensen functional equation in -algebras: a fixed point approachFixed Point Theory and Applications200811 MoslehianMSSuperstability of higher derivations in multi-Banach algebrasTamsui Oxford Journal of Mathematical Sciences200824441742725037071175.39022 Cadariu L, Radu V: Fixed points and the stability of Jensen's functional equation.Journal of Inequalities in Pure and Applied Mathematics 2003,4(1, article 4):-7. RassiasThMFunctional Equations, Inequalities and Applications2003Dordrecht, The NetherlandsKluwer Academic Publishersx+2241047.39001 GavrutaPA generalization of the Hyers-Ulam-Rassias stability of approximately additive mappingsJournal of Mathematical Analysis and Applications19941843431436128151810.1006/jmaa.1994.12110818.46043 GavrutaPAn answer to a question of John M. Rassias concerning the stability of Cauchy equationAdvances in Equations and Inequalities, Hadronic Mathematics Series19996771 ParkCRassiasJMStability of the Jensen-type functional equation in -algebras: a fixed point approachAbstract and Applied Analysis200917 BakerJAThe stability of certain functional equationsProceedings of the American Mathematical Society19911123729732105256810.1090/S0002-9939-1991-1052568-70735.39004 AgarwalRPXuBZhangWStability of functional equations in single variableJournal of Mathematical Analysis and Applications20032882852869202020110.1016/j.jmaa.2003.09.0321053.39042 JungS-MRassiasJMA fixed point approach to the stability of a functional equation of the spiral of TheodorusFixed Point Theory and Applications20087 RassiasThMŠemrlPOn the behavior of mappings which do not satisfy Hyers-Ulam stabilityProceedings of the American Mathematical Society19921144989993105963410.1090/S0002-9939-1992-1059634-10761.47004 UlamSMA Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 81960New York, NY, USAIntersciencexiii+150 GavrutaPOn the Hyers-Ulam-Rassias stability of mappingsRecent Progress in Inequalities, Mathematics and Its Applications1998Dordrecht, The NetherlandsKluwer Academic Publishers46546910.1007/978-94-015-9086-0_27 MoslehianMSNikodemKPopaDAsymptotic aspect of the quadratic functional equation in multi-normed spacesJournal of Mathematical Analysis and Applications20093552717724252174710.1016/j.jmaa.2009.02.0171168.39012 SM Ulam (1250_CR1) 1960 RP Agarwal (1250_CR22) 2003; 288 P Gavruta (1250_CR11) 1999 C Park (1250_CR26) 2009 MS Moslehian (1250_CR18) 2009; 355 T Aoki (1250_CR3) 1950; 2 P Gavruta (1250_CR13) 2004; 9 1250_CR23 L Gavruta (1250_CR15) 2010 P Gavruta (1250_CR10) 1998 ThM Rassias (1250_CR4) 1978; 72 1250_CR28 HG Dales (1250_CR17) 2007; 49 S-M Jung (1250_CR25) 2008 ThM Rassias (1250_CR7) 1992; 114 (1250_CR5) 2003 P Gavruta (1250_CR14) 1995; 2 P Gavruta (1250_CR12) 2001; 261 JB Diaz (1250_CR20) 1968; 74 JA Baker (1250_CR21) 1991; 112 C Park (1250_CR27) 2008 1250_CR16 DH Hyers (1250_CR2) 1941; 27 P Gavruta (1250_CR9) 1997; 42(56) L Cadariu (1250_CR24) 2004 Z Gajda (1250_CR6) 1991; 14 MS Moslehian (1250_CR19) 2008; 24 P Gavruta (1250_CR8) 1994; 184 |
| References_xml | – reference: GavrutaPOn the Hyers-Ulam-Rassias stability of the quadratic mappingsNonlinear Functional Analysis and Applications20049341542821011891066.39029 – reference: ParkCRassiasJMStability of the Jensen-type functional equation in -algebras: a fixed point approachAbstract and Applied Analysis200917 – reference: UlamSMA Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 81960New York, NY, USAIntersciencexiii+150 – reference: RassiasThMFunctional Equations, Inequalities and Applications2003Dordrecht, The NetherlandsKluwer Academic Publishersx+2241047.39001 – reference: RassiasThMOn the stability of the linear mapping in Banach spacesProceedings of the American Mathematical Society197872229730050732710.1090/S0002-9939-1978-0507327-10398.47040 – reference: Dales HG, Polyakov ME: Multi-normed spaces and multi-Banach algebras. preprint – reference: BakerJAThe stability of certain functional equationsProceedings of the American Mathematical Society19911123729732105256810.1090/S0002-9939-1991-1052568-70735.39004 – reference: ParkCAnJSStability of the Cauchy-Jensen functional equation in -algebras: a fixed point approachFixed Point Theory and Applications200811 – reference: MoslehianMSNikodemKPopaDAsymptotic aspect of the quadratic functional equation in multi-normed spacesJournal of Mathematical Analysis and Applications20093552717724252174710.1016/j.jmaa.2009.02.0171168.39012 – reference: GavrutaPAn answer to a question of Th. M. Rassias and J. Tabor on mixed stability of mappingsBuletinul ŞtiinŞific al Universităţii "Politehnica" din Timişoara. Seria Matematică-Fizică199742(56)11616659920983.39012 – reference: Cadariu L, Radu V: Fixed points and the stability of Jensen's functional equation.Journal of Inequalities in Pure and Applied Mathematics 2003,4(1, article 4):-7. – reference: AokiTOn the stability of the linear transformation in Banach spacesJournal of the Mathematical Society of Japan1950264664058010.2969/jmsj/002100640040.35501 – reference: JungS-MRassiasJMA fixed point approach to the stability of a functional equation of the spiral of TheodorusFixed Point Theory and Applications20087 – reference: DalesHGMoslehianMSStability of mappings on multi-normed spacesGlasgow Mathematical Journal2007492321332234726310.1017/S00170895070035521125.39023 – reference: CadariuLRaduVOn the stability of the Cauchy functional equation: a fixed point approachIteration Theory (ECIT '02), Die Grazer Mathematischen Berichte2004Graz, AustriaKarl-Franzens-Universitaet Graz4352 – reference: MoslehianMSSuperstability of higher derivations in multi-Banach algebrasTamsui Oxford Journal of Mathematical Sciences200824441742725037071175.39022 – reference: GavrutaPAn answer to a question of John M. Rassias concerning the stability of Cauchy equationAdvances in Equations and Inequalities, Hadronic Mathematics Series19996771 – reference: HyersDHOn the stability of the linear functional equationProceedings of the National Academy of Sciences of the United States of America194127222224407610.1073/pnas.27.4.2220061.26403 – reference: GajdaZOn stability of additive mappingsInternational Journal of Mathematics and Mathematical Sciences1991143431434111003610.1155/S016117129100056X0739.39013 – reference: GavrutaPOn a problem of G. Isac and Th. M. Rassias concerning the stability of mappingsJournal of Mathematical Analysis and Applications20012612543553185305510.1006/jmaa.2001.75390993.47002 – reference: GavrutaLGavrutaPOn a problem of John M. Rassias concerning the stability in Ulam sense of Euler-Lagrange equationFunctional Equations, Difference Inequalities and Ulam Stability Notions20104753Nova Sciences – reference: GavrutaPHossuMPopescuDCăprăuCOn the stability of mappings and an answer to a problem of Th. M. RassiasAnnales Mathématiques Blaise Pascal199522556010.5802/ambp.4713718920853.46036 – reference: DiazJBMargolisBA fixed point theorem of the alternative, for contractions on a generalized complete metric spaceBulletin of the American Mathematical Society19687430530922026710.1090/S0002-9904-1968-11933-00157.29904 – reference: GavrutaPA generalization of the Hyers-Ulam-Rassias stability of approximately additive mappingsJournal of Mathematical Analysis and Applications19941843431436128151810.1006/jmaa.1994.12110818.46043 – reference: RassiasThMŠemrlPOn the behavior of mappings which do not satisfy Hyers-Ulam stabilityProceedings of the American Mathematical Society19921144989993105963410.1090/S0002-9939-1992-1059634-10761.47004 – reference: Eshaghi-Gordji M, Kaboli-Gharetapeh S, Moslehian MS, Zolfaghari S: Stability of a mixed type additive, quadratic, cubic and quartic functional equation. In Nonlinear Analysis and Variational Problems, Springer Optimization and Its Applications, 35. Edited by: Pardalos PM, Rassias ThM, Khan AA. Springer, Berlin, Germany; 2009:65–80. – reference: GavrutaPOn the Hyers-Ulam-Rassias stability of mappingsRecent Progress in Inequalities, Mathematics and Its Applications1998Dordrecht, The NetherlandsKluwer Academic Publishers46546910.1007/978-94-015-9086-0_27 – reference: AgarwalRPXuBZhangWStability of functional equations in single variableJournal of Mathematical Analysis and Applications20032882852869202020110.1016/j.jmaa.2003.09.0321053.39042 – ident: 1250_CR28 doi: 10.1007/978-1-4419-0158-3_6 – volume: 14 start-page: 431 issue: 3 year: 1991 ident: 1250_CR6 publication-title: International Journal of Mathematics and Mathematical Sciences doi: 10.1155/S016117129100056X – volume: 42(56) start-page: 1 issue: 1 year: 1997 ident: 1250_CR9 publication-title: Buletinul ŞtiinŞific al Universităţii "Politehnica" din Timişoara. 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| Title | Stability of a Mixed Type Functional Equation on Multi-Banach Spaces: A Fixed Point Approach |
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