{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T03:07:24Z","timestamp":1767928044488,"version":"3.49.0"},"reference-count":57,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,19]],"date-time":"2022-11-19T00:00:00Z","timestamp":1668816000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, a new class of real-valued Euler\u2013Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers\u2013Ulam\u2013Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler\u2013Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated.<\/jats:p>","DOI":"10.3390\/sym14112454","type":"journal-article","created":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T03:09:30Z","timestamp":1669000170000},"page":"2454","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Intuitionistic Fuzzy Stability of an Euler\u2013Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2542-3627","authenticated-orcid":false,"given":"P.","family":"Agilan","sequence":"first","affiliation":[{"name":"Department of Mathematics, St. Joseph\u2019s College of Engineering, OMR, Chennai 600119, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3108-9899","authenticated-orcid":false,"given":"K.","family":"Julietraja","sequence":"additional","affiliation":[{"name":"Department of Mathematics, St. Joseph\u2019s College of Engineering, OMR, Chennai 600119, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7986-886X","authenticated-orcid":false,"given":"Nabil","family":"Mlaiki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8798-3297","authenticated-orcid":false,"given":"Aiman","family":"Mukheimer","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s00010-016-0421-3","article-title":"A note on solutions of a functional equation arising in a queuing model for a LAN gateway","volume":"90","year":"2016","journal-title":"Aequationes Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s00010-017-0471-1","article-title":"On the structure and solutions of functional equations arising from queueing models","volume":"91","author":"Nassar","year":"2017","journal-title":"Aequationes Math."},{"key":"ref_3","first-page":"363","article-title":"On a functional equation arising from a network model","volume":"11","author":"Nassar","year":"2017","journal-title":"Appl. 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