{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:38:06Z","timestamp":1777423086468,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,25]],"date-time":"2023-06-25T00:00:00Z","timestamp":1687651200000},"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":["Symmetry"],"abstract":"<jats:p>The main objective of this paper is to present classical second-order differential subordination knowledge extended in this study to include new results regarding third-order differential subordinations. The focus of this study is on the main problems examined by differential subordination theory. Hence, the new results obtained here reveal techniques for identifying dominants and the best dominant of certain third-order differential subordinations. Another aspect of novelty is the new application of the Gaussian hypergeometric function. Novel third-order differential subordination results are obtained using the best dominant provided by the theorems and the operator previously defined as Gaussian hypergeometric function\u2019s fractional integral. The research investigation is concluded by giving an example of how the results can be implemented.<\/jats:p>","DOI":"10.3390\/sym15071306","type":"journal-article","created":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T02:05:02Z","timestamp":1687745102000},"page":"1306","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["New Applications of Gaussian Hypergeometric Function for Developments on Third-Order Differential Subordinations"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2902-4455","authenticated-orcid":false,"given":"Georgia Irina","family":"Oros","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1000-094X","authenticated-orcid":false,"given":"Gheorghe","family":"Oros","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9215-2404","authenticated-orcid":false,"given":"Lavinia Florina","family":"Preluca","sequence":"additional","affiliation":[{"name":"Doctoral School of Engineering Sciences, University of Oradea, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,25]]},"reference":[{"key":"ref_1","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_2","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_3","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_4","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Theory and Applications, Marcel Dekker, Inc."},{"key":"ref_5","unstructured":"Pommerenke, C. (1975). Univalent Functions, Vandenhoeck and Ruprecht."},{"key":"ref_6","first-page":"187","article-title":"Third-order differential subordination of analytic function","volume":"35","author":"Jeyaraman","year":"2013","journal-title":"Acta Univ. Apulensis"},{"key":"ref_7","first-page":"76","article-title":"Certain third-order differential subordination and superordination results of meromorphic multivalent functions","volume":"2","author":"Farzana","year":"2015","journal-title":"Asia Pac. J. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1707","DOI":"10.1016\/S0252-9602(14)60116-8","article-title":"Third-order differential subordination results for analytic functions involving the generalized Bessel functions","volume":"34","author":"Tang","year":"2014","journal-title":"Acta Math. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1007\/s40840-014-0108-7","article-title":"Third-Order Differential Superordination Involving the Generalized Bessel Functions","volume":"38","author":"Tang","year":"2014","journal-title":"Bull. Malays. Math. Sci. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"792175","DOI":"10.1155\/2014\/792175","article-title":"Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator","volume":"2014","author":"Tang","year":"2014","journal-title":"Abstr. Appl. Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1515\/math-2015-0068","article-title":"The Third-Order Differential Subordination and Superordination involving a fractional operator","volume":"13","author":"Ibrahim","year":"2015","journal-title":"Open Math."},{"key":"ref_12","first-page":"819","article-title":"Third-order differential Sandwich type outcome involving a certain linear operator on meromorphic multivalent functions","volume":"118","author":"Ghanim","year":"2018","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_13","first-page":"63","article-title":"Third-order differential sandwich-type result of meromorphic p-valent functions associated with a certain linear operator","volume":"22","author":"Ghanim","year":"2018","journal-title":"Commun. Appl. Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"469","DOI":"10.18576\/amis\/120301","article-title":"Third-order differential subordination and differential superordination results for analytic functions involving the Srivastava-Attiya operator","volume":"12","author":"Srivastava","year":"2018","journal-title":"Appl. Math. Inf. Sci."},{"key":"ref_15","first-page":"1","article-title":"Some third-order differential subordination and superordination results of some meromorphic functions using a Hurwitz-Lerech Zeta type operator","volume":"4","author":"Hassan","year":"2015","journal-title":"Ilirias J. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s00009-017-0969-8","article-title":"Third-order differential subordinations for analytic functions associated with generalized Mittag-Leffler functions","volume":"14","year":"2017","journal-title":"Mediterr. J. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1186\/s13660-019-2198-0","article-title":"Applications of differential subordinations involving a generalized fractional differintegral operator","volume":"2019","author":"Zayed","year":"2019","journal-title":"J. Inequal. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Atshan, W.G., Hiress, R.A., and Alt\u0131nkaya, S. (2022). On Third-Order Differential Subordination and Superordination Properties of Analytic Functions Defined by a Generalized Operator. Symmetry, 14.","DOI":"10.3390\/sym14020418"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Al-Janaby, H., Ghanim, F., and Darus, M. (2020). On The Third-Order Complex Differential Inequalities of \u03be-Generalized-Hurwitz\u2013Lerch Zeta Functions. Mathematics, 8.","DOI":"10.3390\/math8050845"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Attiya, A.A., Seoudy, T.M., and Albaid, A. (2023). Third-Order Differential Subordination for Meromorphic Functions Associated with Generalized Mittag-Leffler Function. Fractal Fract., 7.","DOI":"10.3390\/fractalfract7020175"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Oros, G.I., Oros, G., and Preluca, L.F. (2023). Third-Order Differential Subordinations Using Fractional Integral of Gaussian Hypergeometric Function. Axioms, 12.","DOI":"10.3390\/axioms12020133"},{"key":"ref_22","first-page":"53","article-title":"On the distortion theorems I","volume":"18","author":"Owa","year":"1978","journal-title":"Kyungpook Math. J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.4153\/CJM-1987-054-3","article-title":"Univalent and starlike generalized hypergeometric functions","volume":"39","author":"Owa","year":"1987","journal-title":"Can. J. Math."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Oros, G.I., and Dzitac, S. (2022). Applications of Subordination Chains and Fractional Integral in Fuzzy Differential Subordinations. Mathematics, 10.","DOI":"10.3390\/math10101690"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Oros, G.I. (2021). Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities. Symmetry, 13.","DOI":"10.3390\/sym13050904"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"13143","DOI":"10.3934\/math.2021759","article-title":"Carath\u00e9odory properties of Gaussian hypergeometric function associated with differential inequalities in the complex plane","volume":"6","author":"Oros","year":"2021","journal-title":"AIMS Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"11269","DOI":"10.1002\/mma.7486","article-title":"Third-order differential subordinations for multivalent functions in the theory of source-sink dynamics","volume":"44","author":"Morais","year":"2021","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Darweesh, A.M., Atshan, W.G., Battor, A.H., and Lupa\u015f, A.A. (2022). Third-Order Differential Subordination Results for Analytic Functions Associated with a Certain Differential Operator. Symmetry, 14.","DOI":"10.3390\/sym14010099"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s13370-023-01066-4","article-title":"Some applications of third-order differential subordination for analytic functions involving k-Ruscheweyh derivative operator","volume":"34","author":"Seoudy","year":"2023","journal-title":"Afr. Mat."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"45","DOI":"10.13164\/ma.2022.05","article-title":"Third order differential subordination associated with Janowski functions","volume":"11","author":"Jeyaraman","year":"2022","journal-title":"Math. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"060055","DOI":"10.1063\/5.0093563","article-title":"Third-order sandwich results for analytic functions defined by generalized operator","volume":"2398","author":"ASaeed","year":"2022","journal-title":"AIP Conf. Proc."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"040021","DOI":"10.1063\/5.0134582","article-title":"Third order differential super ordination and sub-ordination results for multivalent meromorphically functions associated with Wright function","volume":"2414","author":"Taha","year":"2023","journal-title":"AIP Conf. Proc."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3901","DOI":"10.1016\/j.aej.2021.02.037","article-title":"Applications of differential subordination and superordination theorems to fluid mechanics involving a fractional higher-order integral operator","volume":"60","author":"Morais","year":"2021","journal-title":"Alex. Eng. 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