{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:27:13Z","timestamp":1740140833125,"version":"3.37.3"},"reference-count":16,"publisher":"IOP Publishing","issue":"1","license":[{"start":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T00:00:00Z","timestamp":1593561600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"},{"start":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T00:00:00Z","timestamp":1593561600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["J. Phys.: Conf. Ser."],"published-print":{"date-parts":[[2020,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, the authors proved the generalized U-H stability of quadratic functional equation of the form <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mtable columnalign=\"left\">\n                           <mml:mtr>\n                              <mml:mtd>\n                                 <mml:mi>f<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">(<\/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:mn>3<\/mml:mn>\n                                 <mml:mi>z<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                 <mml:mo>\u2212<\/mml:mo>\n                                 <mml:mi>f<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                 <mml:mi>x<\/mml:mi>\n                                 <mml:mo>\u2212<\/mml:mo>\n                                 <mml:mi>y<\/mml:mi>\n                                 <mml:mo>+<\/mml:mo>\n                                 <mml:mn>3<\/mml:mn>\n                                 <mml:mi>z<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                 <mml:mo>\u2212<\/mml:mo>\n                                 <mml:mi>f<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                 <mml:mi>x<\/mml:mi>\n                                 <mml:mo>+<\/mml:mo>\n                                 <mml:mi>y<\/mml:mi>\n                                 <mml:mo>\u2212<\/mml:mo>\n                                 <mml:mn>3<\/mml:mn>\n                                 <mml:mi>z<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                 <mml:mo>\u2212<\/mml:mo>\n                                 <mml:mi>f<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                 <mml:mo>\u2212<\/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:mn>3<\/mml:mn>\n                                 <mml:mi>z<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                 <mml:mo>=<\/mml:mo>\n                                 <mml:mi>f<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                 <mml:mi>x<\/mml:mi>\n                                 <mml:mo>+<\/mml:mo>\n                                 <mml:mi>y<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                 <mml:mo>+<\/mml:mo>\n                                 <mml:mn>6<\/mml:mn>\n                                 <mml:mi>f<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                 <mml:mi>y<\/mml:mi>\n                                 <mml:mo>+<\/mml:mo>\n                                 <mml:mi>z<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <\/mml:mtd>\n                           <\/mml:mtr>\n                           <mml:mtr>\n                              <mml:mtd>\n                                 <mml:mspace width=\"7em\"\/>\n                                 <mml:mo>+<\/mml:mo>\n                                 <mml:mn>6<\/mml:mn>\n                                 <mml:mi>f<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                 <mml:mi>x<\/mml:mi>\n                                 <mml:mo>+<\/mml:mo>\n                                 <mml:mi>z<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                 <mml:mo>\u2212<\/mml:mo>\n                                 <mml:mn>9<\/mml:mn>\n                                 <mml:mi>f<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                 <mml:mi>x<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                 <mml:mo>\u2212<\/mml:mo>\n                                 <mml:mn>9<\/mml:mn>\n                                 <mml:mi>f<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                 <mml:mi>y<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                 <mml:mo>\u2212<\/mml:mo>\n                                 <mml:mn>30<\/mml:mn>\n                                 <mml:mi>f<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                 <mml:mi>z<\/mml:mi>\n                                 <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <\/mml:mtd>\n                           <\/mml:mtr>\n                        <\/mml:mtable>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"JPCS_1597_1_012002_ieqn1.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula> in Banach space using direct method.<\/jats:p>","DOI":"10.1088\/1742-6596\/1597\/1\/012002","type":"journal-article","created":{"date-parts":[[2020,8,21]],"date-time":"2020-08-21T01:13:30Z","timestamp":1597972410000},"page":"012002","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Hyers -Ulam stability of quadratic functional equation"],"prefix":"10.1088","volume":"1597","author":[{"given":"Vediyappan","family":"Govindan","sequence":"first","affiliation":[]},{"given":"Sandra","family":"Pinelas","sequence":"additional","affiliation":[]}],"member":"266","reference":[{"year":"1989","author":"Aczel","key":"JPCS_1597_1_012002bib1"},{"key":"JPCS_1597_1_012002bib2","doi-asserted-by":"crossref","first-page":"64","DOI":"10.2969\/jmsj\/00210064","article-title":"On the stability of the linear transformation in Banach spaces","volume":"2","author":"Aoki","year":"1950","journal-title":"J. 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