{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:10:14Z","timestamp":1760231414979,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,16]],"date-time":"2022-09-16T00:00:00Z","timestamp":1663286400000},"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>The research presented in this paper deals with analytic p-valent functions related to the generalized probability distribution in the open unit disk U. Using the Hadamard product or convolution, function fs(z) is defined as involving an analytic p-valent function and generalized distribution expressed in terms of analytic p-valent functions. Neighborhood properties for functions fs(z) are established. Further, by applying a previously introduced linear transformation to fs(z) and using an extended Libera integral operator, a new generalized Libera-type operator is defined. Moreover, using the same linear transformation, subclasses of starlike, convex, close-to-convex and spiralike functions are defined and investigated in order to obtain geometrical properties that characterize the new generalized Libera-type operator. Symmetry properties are due to the involvement of the Libera integral operator and convolution transform.<\/jats:p>","DOI":"10.3390\/sym14091934","type":"journal-article","created":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T04:28:55Z","timestamp":1663648135000},"page":"1934","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Application of a Multiplier Transformation to Libera Integral Operator Associated with Generalized Distribution"],"prefix":"10.3390","volume":"14","author":[{"given":"Jamiu","family":"Hamzat","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Lagos, Lagos 101017, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6472-2430","authenticated-orcid":false,"given":"Abiodun","family":"Oladipo","sequence":"additional","affiliation":[{"name":"Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso 210214, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2902-4455","authenticated-orcid":false,"given":"Georgia","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"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Guney, H.O., Oros, G.I., and Owa, S. (2022). An application of S\u0103l\u0103gean operator concerning starlike functions. Axioms, 11.","DOI":"10.3390\/axioms11020050"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"499","DOI":"10.46793\/KgJMat2104.499J","article-title":"A subclass of Noor-type harmonic p-valent functions based on hypergeometric functions","volume":"45","author":"Ghanim","year":"2021","journal-title":"Kragujev. J. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s13370-020-00825-x","article-title":"On a class of p-valent functions involving generalized differential operator","volume":"32","author":"Yousef","year":"2021","journal-title":"Afr. Mat."},{"key":"ref_4","first-page":"6","article-title":"Some properties on a class of p-valent functions involving generalized differential operator","volume":"18","author":"Yousef","year":"2021","journal-title":"Aust. J. Math. Anal. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2150084","DOI":"10.1142\/S1793557121500844","article-title":"Some properties of p-valent analytic functions defined by Dziok-Srivastava operator","volume":"14","author":"Ali","year":"2021","journal-title":"Asian-Eur. J. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2018\/8654506","article-title":"Generalized distribution and its geometric properties associated with univalent functions","volume":"2018","author":"Porwal","year":"2018","journal-title":"J. Complex Anal."},{"key":"ref_7","first-page":"19","article-title":"Bounds for Probabilities of the Generalized Distribution Defined by Generalized Polylogarithm","volume":"51","author":"Oladipo","year":"2019","journal-title":"J. Math. Punjab Univ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1016\/j.camwa.2007.05.010","article-title":"On a subclasses of n-p-valent prestarlike functions","volume":"55","author":"Aouf","year":"2008","journal-title":"Comput. Math. Appl."},{"key":"ref_9","unstructured":"C\u0103ta\u015f, A. (2007, January 20\u201324). On certain class of p-valent functions defined by new multiplier transformations. Proceedings of the International Symposium on Geometric Functions Theory and Applications, Istanbul, Turkey."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"53","DOI":"10.4134\/BKMS.2004.41.1.053","article-title":"On a subclasses of certain starlike functions with negative coefficients","volume":"41","author":"Kamali","year":"2004","journal-title":"Bull. Korean Math. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1090\/S0002-9939-1965-0178131-2","article-title":"Some classes of regular univalent functions","volume":"16","author":"Libera","year":"1965","journal-title":"Proc. Math. Soc."},{"key":"ref_12","unstructured":"Hamzat, J.O., and El-Ashwah, R.M. (Ukraine J. Math., 2021). Some properties of a generalized multiplier transform on analytic p-valent functions, Ukraine J. Math., accepted."},{"key":"ref_13","first-page":"157","article-title":"Differential Subordinations and univalent functions","volume":"28","author":"Miller","year":"1981","journal-title":"J. Inequalities Pure Appl. Math."},{"key":"ref_14","first-page":"1","article-title":"Inclusion and neighbourhood properties of certain subclasses of multivalent functions of complex order","volume":"7","author":"Srivastava","year":"2006","journal-title":"JIPAM"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/978-3-0348-6290-5_26","article-title":"On a Briot-Bouquet differential subordination","volume":"Volume 64","author":"Eenigenburg","year":"1983","journal-title":"General Inequalities 3"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Differential Subordinations in Theory and Applications, Marcel Dekker, Inc.","DOI":"10.1201\/9781482289817"},{"key":"ref_17","first-page":"27","article-title":"Subordination properties of certain subclasses of p-valent functions defined by an integral operator","volume":"71","author":"Seoudy","year":"2016","journal-title":"Le Matematiche"},{"key":"ref_18","first-page":"1751","article-title":"Inclusion Properties of Certain Subclasses of Analytic Functions","volume":"7","author":"Swamy","year":"2012","journal-title":"Int. Math. Forum"},{"key":"ref_19","first-page":"109","article-title":"A new multiplier differential operator","volume":"7","author":"Makinde","year":"2018","journal-title":"Adv. Math. Sci. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"12","DOI":"10.2307\/2007212","article-title":"Functions which map the interior of the unit circle upon simple region","volume":"17","author":"Alexander","year":"1915","journal-title":"Ann. Math."},{"key":"ref_21","unstructured":"Bulboaca, T. (2005). Differential Subordinations and Superordinations. Recent Results, House of Scientific Book Publishing."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1016\/S0022-247X(02)00500-0","article-title":"Some inclusion properties of a family of integral operator","volume":"276","author":"Choi","year":"2002","journal-title":"J. Math. Anal. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1080\/02781070500302520","article-title":"Convexity condition for the Libera integral operator","volume":"51","author":"Oros","year":"2006","journal-title":"Complex Var. Elliptic Equations"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"303","DOI":"10.18514\/MMN.2020.3084","article-title":"New differential subordination obtained by using a differential-integral Ruscheweyh-Libera operator","volume":"21","author":"Oros","year":"2020","journal-title":"Miskolc Math. Notes"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1186\/s13662-021-03497-4","article-title":"Study on new integral operators defined unig confluent hypergeometric function","volume":"2021","author":"Oros","year":"2021","journal-title":"Adv. Differ. Equ."},{"key":"ref_26","first-page":"2161","article-title":"(\u03b8,\u03bc,\u03c4)-Neighborhood for certain functions involving modified sigmoid function","volume":"68","author":"Orhan","year":"2019","journal-title":"Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat."},{"key":"ref_27","unstructured":"Orhan, H., Kadoiglu, E., and Owa, S. (2007, January 20\u201324). (\u03b8,\u03bc)- Neighborhoods for certain analytic functions. Proceedings of the International Symposium on Geometric Functions Theory and Applications, Istanbul, Turkey."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/9\/1934\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:33:07Z","timestamp":1760142787000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/9\/1934"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,16]]},"references-count":27,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["sym14091934"],"URL":"https:\/\/doi.org\/10.3390\/sym14091934","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,9,16]]}}}