{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:45:45Z","timestamp":1777704345131,"version":"3.51.4"},"reference-count":38,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2020,3,18]],"date-time":"2020-03-18T00:00:00Z","timestamp":1584489600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2020,4,30]]},"abstract":"<jats:p>\n                    Let\n                    <jats:italic>k<\/jats:italic>\n                    \u00a0\u2265\u00a02 be an integer. The purpose of this paper is first to introduce the notation of Felbin\u2019s type fuzzy normed linear spaces, and then by virtue of this notation to study some stability results concerning the more general cubic functional equation of the form\n                    <jats:disp-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mtable>\n                          <mml:mtr>\n                            <mml:mtd columnalign=\"right\">\n                              <mml:mi>f<\/mml:mi>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>x<\/mml:mi>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mi mathvariant=\"italic\">ky<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mi>f<\/mml:mi>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>x<\/mml:mi>\n                            <\/mml:mtd>\n                            <mml:mtd columnalign=\"left\">\n                              <mml:mo>-<\/mml:mo>\n                              <mml:mi mathvariant=\"italic\">ky<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mi>f<\/mml:mi>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi mathvariant=\"italic\">kx<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mtd>\n                          <\/mml:mtr>\n                          <mml:mtr>\n                            <mml:mtd columnalign=\"right\"\/>\n                            <mml:mtd columnalign=\"left\">\n                              <mml:mo>=<\/mml:mo>\n                              <mml:msup>\n                                <mml:mi>k<\/mml:mi>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:msup>\n                              <mml:mi>f<\/mml:mi>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>x<\/mml:mi>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mi>y<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:msup>\n                                <mml:mi>k<\/mml:mi>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:msup>\n                              <mml:mi>f<\/mml:mi>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>x<\/mml:mi>\n                              <mml:mo>-<\/mml:mo>\n                              <mml:mi>y<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:msup>\n                                <mml:mi>k<\/mml:mi>\n                                <mml:mn>3<\/mml:mn>\n                              <\/mml:msup>\n                              <mml:mo>-<\/mml:mo>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:msup>\n                                <mml:mi>k<\/mml:mi>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:msup>\n                              <mml:mo>+<\/mml:mo>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mo>)<\/mml:mo>\n                              <mml:mi>f<\/mml:mi>\n                              <mml:mo>(<\/mml:mo>\n                              <mml:mi>x<\/mml:mi>\n                              <mml:mo>)<\/mml:mo>\n                            <\/mml:mtd>\n                          <\/mml:mtr>\n                        <\/mml:mtable>\n                      <\/mml:math>\n                    <\/jats:disp-formula>\n                    in the setting of Felbin\u2019s type fuzzy normed linear spaces by employing the direct and fixed point methods. Then some applications of our results for the stability of the cubic functional equation from a real normed space to a Banach space will be demonstrated. Furthermore, the interdisciplinary relation between the theory of Felbin\u2019s type fuzzy spaces and the theory of functional equations are also presented in this paper.\n                  <\/jats:p>","DOI":"10.3233\/jifs-191418","type":"journal-article","created":{"date-parts":[[2020,3,20]],"date-time":"2020-03-20T13:44:12Z","timestamp":1584711852000},"page":"4733-4742","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Stability of a more general cubic functional equation in Felbin\u2019s type fuzzy normed linear spaces"],"prefix":"10.1177","volume":"38","author":[{"given":"Zhihua","family":"Wang","sequence":"first","affiliation":[{"name":"School of Science, Hubei University of Technology, Wuhan, Hubei, P.R. 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