{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T15:32:54Z","timestamp":1767108774570,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T00:00:00Z","timestamp":1722211200000},"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>This paper contains several novel definitions including neutrosophic E\u03b2 metric space, neutrosophic quasi-S\u03b2-metric space, neutrosophic pseudo-S\u03b2-metric space, neutrosophic quasi-E-metric space and neutrosophic pseudo-E\u03b2-metric space. Further, we present some generalized fixed point results with non-trivial examples and the decomposition theorem in the setting of the neutrosophic pseudo-E\u03b2-metric space. Moreover, by using the main result, we examine the existence and uniqueness of the solution to an integral equation, a system of linear equations, and nonlinear fractional differential equations.<\/jats:p>","DOI":"10.3390\/sym16080965","type":"journal-article","created":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T15:26:53Z","timestamp":1722526013000},"page":"965","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Some Generalized Neutrosophic Metric Spaces and Fixed Point Results with Applications"],"prefix":"10.3390","volume":"16","author":[{"given":"Mohammad","family":"Akram","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Umar","family":"Ishtiaq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 15320, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khaleel","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3223-320X","authenticated-orcid":false,"given":"Tania A.","family":"Laz\u0103r","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Technical University of Cluj Napoca, 400114 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vasile L.","family":"Laz\u0103r","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Technical University of Cluj Napoca, 400114 Cluj-Napoca, Romania"},{"name":"Department of Economic and Technical Sciences, Vasile Goldi\u0219 Western University of Arad, 310025 Arad, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8304-1574","authenticated-orcid":false,"given":"Liliana","family":"Guran","sequence":"additional","affiliation":[{"name":"Department of Hospitality Services, Babe\u0219-Bolyai University, Horea Street, no. 7, 400174 Cluj-Napoca, Romania"},{"name":"Computer Science Department, Technical University of Cluj Napoca, 400027 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1002\/mana.19630260109","article-title":"2-metrische R\u00e4ume und ihre topologische Struktur","volume":"26","year":"1963","journal-title":"Math. 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