{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:16:12Z","timestamp":1760058972375,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,17]],"date-time":"2025-05-17T00:00:00Z","timestamp":1747440000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Oradea, Romania"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This work\u2019s theorems and corollaries present new third-order fuzzy differential subordination and superordination results developed by using a novel convolution linear operator involving the Gaussian hypergeometric function and a previously studied operator. The paper reveals methods for finding the best dominant and best subordinant for the third-order fuzzy differential subordinations and superordinations, respectively. The investigation concludes with the assertion of sandwich-type theorems connecting the conclusions of the studies conducted using the particular methods of the theories of the third-order fuzzy differential subordination and superordination, respectively.<\/jats:p>","DOI":"10.3390\/axioms14050378","type":"journal-article","created":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T06:31:29Z","timestamp":1747636289000},"page":"378","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Third-Order Fuzzy Subordination and Superordination on Analytic Functions on Punctured Unit Disk"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5477-0065","authenticated-orcid":false,"given":"Ekram E.","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 81451, Saudi Arabia"},{"name":"Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said 42521, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2902-4455","authenticated-orcid":false,"given":"Georgia Irina","family":"Oros","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5490-3745","authenticated-orcid":false,"given":"Rabha M.","family":"El-Ashwah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7619-6869","authenticated-orcid":false,"given":"Abeer M.","family":"Albalahi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 81451, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.15672\/hujms.1319541","article-title":"Introduction in third-order fuzzy differential subordination","volume":"53","author":"Oros","year":"2024","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_2","first-page":"55","article-title":"Fuzzy differential subordination","volume":"3","author":"Oros","year":"2012","journal-title":"ActaUniv. Apulensis"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Abdulnabi, F.F., Al-Janaby, H.F., Ghanim, F., and Alb Lupa\u0219, A. (2023). Some results on third-order differential subordination and differential superordination for analytic functions using a fractional differential operator. Mathematics, 11.","DOI":"10.3390\/math11184021"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6576","DOI":"10.24996\/ijs.2024.65.11.32","article-title":"Admissible Classes of Seven-Parameter Mittag-Leffler Operator with Third-Order Differential Subordination Properties","volume":"65","author":"Rasheed","year":"2024","journal-title":"Iraqi J. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"070016","DOI":"10.1063\/5.0256514","article-title":"Third order differential subordination results for holomorphic functions involving convolution operator","volume":"3169","author":"Ahmed","year":"2025","journal-title":"AIP Conf. Proc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1080\/17476931003728404","article-title":"Third-order differential inequalities and subordinations in the complex plane","volume":"56","author":"Antonino","year":"2011","journal-title":"Complex Var. Elliptic Equ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/0022-247X(78)90181-6","article-title":"Second order-differential inequalities in the complex plane","volume":"65","author":"Miller","year":"1978","journal-title":"J. Math. Anal. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1307\/mmj\/1029002507","article-title":"Differential subordinations and univalent functions","volume":"28","author":"Miller","year":"1981","journal-title":"Michig. Math. J."},{"key":"ref_9","first-page":"27","article-title":"Fuzzy Differential Superordination","volume":"7","author":"Atshan","year":"2017","journal-title":"Theory Appl. Math. Comput. Sci."},{"key":"ref_10","first-page":"815","article-title":"Subordinations of differential superordinations","volume":"48","author":"Miller","year":"2003","journal-title":"Complex Var."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Oros, G.I., Dzitac, S., and Bardac-Vlada, D.A. (2024). Introducing the Third-Order Fuzzy Superordination Concept and Related Results. Mathematics, 12.","DOI":"10.3390\/math12193095"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy Sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_13","first-page":"1476","article-title":"A note on special fuzzy differential subordinations using generalized S\u0103l\u0103gean operator and Ruscheweyh derivative","volume":"15","year":"2013","journal-title":"J. Comput. Anal. Appl."},{"key":"ref_14","first-page":"167","article-title":"On special fuzzy differential subordination using Ruscheweyh operator","volume":"22","author":"Venter","year":"2015","journal-title":"An. Univ. Oradea Fasc. Mat."},{"key":"ref_15","first-page":"921","article-title":"Fuzzy subordination and superordination results for certain subclasses of analytic functions associated with Srivastava-Attitya operator","volume":"118","author":"Thilagavathi","year":"2018","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"15569","DOI":"10.3934\/math.2023794","article-title":"Fuzzy differential subordination and superordination results for q-analogue of multiplier transformation","volume":"8","author":"Shah","year":"2023","journal-title":"AIMS Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"21053","DOI":"10.3934\/math.20241023","article-title":"Fuzzy differential subordination and superordination results for the Mittag-Leffler type Pascal distribution","volume":"9","author":"Soren","year":"2024","journal-title":"AIMS Math."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.46481\/jnsps.2024.1832","article-title":"Differential and fuzzy differential sandwich theorems involving quantum calculus operators","volume":"6","author":"Silviya","year":"2024","journal-title":"J. Niger. Soc. Phys. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"040028","DOI":"10.1063\/5.0202876","article-title":"The admissible method for complex formula of operator on meromorphic functions","volume":"3036","author":"Moureh","year":"2024","journal-title":"AIP Conf. Proc."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ali, E.E., Oros, G.I., El-Ashwah, R.M., Albalahi, A.M., and Ennaceur, M. (2024). Fuzzy Subordination Results for Meromorphic Functions Associated with Hurwitz\u2013Lerch Zeta Function. Mathematics, 12.","DOI":"10.3390\/math12233721"},{"key":"ref_21","first-page":"48","article-title":"Sandwich results for p-valent meromorphic functions associated with Hurwitz-Lerch Zeta function","volume":"32","year":"2018","journal-title":"Tamsui Oxford J. Infor. Math. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Differential Subordinations: Theory and Applications, Marcel Dekker Inc.","DOI":"10.1201\/9781482289817"},{"key":"ref_23","first-page":"111","article-title":"Certain integral operators applied to p-valent functions","volume":"24","author":"Aqlan","year":"2003","journal-title":"J. Nat. Geom."},{"key":"ref_24","first-page":"53","article-title":"Applications of differential subordination on certain class of meromorphic p-valent functions associated with certain integral operator","volume":"31","author":"Aouf","year":"2012","journal-title":"Acta Univ. Apulensis"},{"key":"ref_25","first-page":"191","article-title":"Inclusion relationships properties for certain subclasses of meromorphic functions associated with Hurwitz-Lerech Zeta function","volume":"34","year":"2013","journal-title":"Acta Univ. Apulensis"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Khan, S., Ro, J.-S., Tchier, F., and Khan, N. (2023). Applications of Fuzzy Differential Subordination for a New Subclass of Analytic Functions. Axioms, 12.","DOI":"10.3390\/axioms12080745"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Breaz, D., Khan, S., Tawfiq, F.M.O., and Tchier, F. (2023). Applications of Fuzzy Differential Subordination to the Subclass of Analytic Functions Involving Riemann\u2013Liouville Fractional Integral Operator. Mathematics, 11.","DOI":"10.3390\/math11244975"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2170371","DOI":"10.1080\/27690911.2023.2170371","article-title":"Fuzzy differential subordination related to strongly Janowski functions","volume":"31","author":"Kanwal","year":"2023","journal-title":"Appl. Math. Sci. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"080022","DOI":"10.1063\/5.0161576","article-title":"Fuzzy differential subordinations and superordinations for univalent functions involving linear operator","volume":"2834","author":"Salih","year":"2023","journal-title":"AIP Conf. Proc."},{"key":"ref_30","first-page":"1","article-title":"Fuzzy Differential Subordinations for Univalent Functions Involving Rafid-Operator","volume":"32","year":"2024","journal-title":"J. Eg. Math. Soc."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/378\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:34:28Z","timestamp":1760031268000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/378"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,17]]},"references-count":30,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["axioms14050378"],"URL":"https:\/\/doi.org\/10.3390\/axioms14050378","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,5,17]]}}}