{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T09:19:07Z","timestamp":1762075147261,"version":"build-2065373602"},"reference-count":10,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T00:00:00Z","timestamp":1668038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The present paper deals with a new differential operator denoted by Fp,t\u03b4,n,b,c,m,\u03b2, whose certain properties are deduced by using well-known earlier studies regarding differential inequalities and the Caratheodory function. The new introduced operator is defined by making use of a linear combination of the binomial series and confluent hypergeometric function. In addition, by using special values of the parameters, we establish certain results concretized in specific corollaries, which provide useful inequalities. Studying these properties by using various types of operators is a technique that is widely used.<\/jats:p>","DOI":"10.3390\/axioms11110631","type":"journal-article","created":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T02:07:48Z","timestamp":1668046068000},"page":"631","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Some Inequalities for Certain p-Valent Functions Connected with the Combination Binomial Series and Confluent Hypergeometric Function"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4052-391X","authenticated-orcid":false,"given":"Sheza M.","family":"El-Deeb","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt"},{"name":"Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 52222, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1000-7375","authenticated-orcid":false,"given":"Adriana","family":"C\u0103ta\u015f","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF02392821","article-title":"A proof of the Bieberbach conjecture","volume":"154","author":"Branges","year":"1985","journal-title":"Acta Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3605","DOI":"10.1002\/mma.6966","article-title":"An analytical study on Mittag-Leffler confluent hypergeometric functions with fractional integral operator","volume":"44","author":"Ghanim","year":"2020","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Oros, G.I. (2021). New Conditions for Univalence of Confluent Hypergeometric Function. Symmetry, 13.","DOI":"10.3390\/sym13010082"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s13370-016-0422-3","article-title":"Confluent hypergeometric distribution and its applications on certain classes of univalent functions","volume":"28","author":"Porwal","year":"2017","journal-title":"Afr. Mat."},{"key":"ref_5","unstructured":"Rainville, E.D. (1960). Special Functions, The Macmillan Co."},{"key":"ref_6","first-page":"327","article-title":"On unified subclass of complex order connected with q-confluent hypergeometric distribution","volume":"16","year":"2022","journal-title":"Surv. Math. Appl."},{"key":"ref_7","first-page":"82","article-title":"Subclasses of bi-univalent functions associated with q-confluent hypergeometric distribution based upon the Horadam polynomials","volume":"1","year":"2021","journal-title":"Adv. Theory Nonlinear Anal."},{"key":"ref_8","first-page":"495","article-title":"Confluent hypergeometric distribution and its applications on certain classes of univalent functions of conic regions","volume":"58","author":"Porwal","year":"2018","journal-title":"Kyungpook Math. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"289","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_10","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1090\/S0002-9904-1975-13643-3","article-title":"Differential inequalities and Caratheodory function","volume":"8","author":"Miller","year":"1975","journal-title":"Bull. Am. Math. Soc."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/11\/631\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:13:34Z","timestamp":1760145214000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/11\/631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,10]]},"references-count":10,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["axioms11110631"],"URL":"https:\/\/doi.org\/10.3390\/axioms11110631","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,11,10]]}}}