{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:46:31Z","timestamp":1760060791969,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T00:00:00Z","timestamp":1758672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IMSIU-DDRSP2504"],"award-info":[{"award-number":["IMSIU-DDRSP2504"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper introduces a novel generalized q-symmetric differential operator for studying a certain subclass of univalent functions with negative coefficients. We establish several significant theoretical results for this class, including sharp coefficient bounds and characterization theorems based on the generalized Hadamard product. Two significant applications demonstrate the theoretical framework\u2019s practical utility. First, in the context of geometric modeling, we demonstrate how the function class and operator can be utilized to create and control complex, non-overlapping transformations. Second, in digital signal processing, we show that these functions serve as stable digital filter prototypes and that our operator is an effective tool for fine-tuning the filter\u2019s frequency response. These applications bridge the gap between abstract geometric function theory and practical system design by demonstrating the operator\u2019s versatility as a tool for analysis and synthesis.<\/jats:p>","DOI":"10.3390\/sym17101593","type":"journal-article","created":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T10:39:42Z","timestamp":1758710382000},"page":"1593","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Geometric Properties and Applications in System Modeling for a Generalized q-Symmetric Operator"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6963-0847","authenticated-orcid":false,"given":"Abdelrahman M.","family":"Yehia","sequence":"first","affiliation":[{"name":"Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62611, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7676-1020","authenticated-orcid":false,"given":"Atef F.","family":"Hashem","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. S.","family":"Al-Moisheer","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5971-0048","authenticated-orcid":false,"given":"Mohamed A.","family":"Sohaly","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samar M.","family":"Madian","sequence":"additional","affiliation":[{"name":"Basic Science Department, Higher Institute of Engineering and Technology, New Damietta 34517, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammed M.","family":"Tharwat","sequence":"additional","affiliation":[{"name":"Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62611, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"87","DOI":"10.4064\/ap-56-1-87-92","article-title":"On uniformly convex functions","volume":"56","author":"Goodman","year":"1991","journal-title":"Ann. 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