{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T20:50:28Z","timestamp":1781729428794,"version":"3.54.5"},"reference-count":71,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T00:00:00Z","timestamp":1749081600000},"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>This work introduces a novel family of analytic and univalent functions formulated through the integration of Gregory coefficients and Sakaguchi-type functions. Employing subordination techniques, we obtain sharp bounds for the initial coefficients in their Taylor expansions. The influence of parameter variations is examined through comprehensive geometric visualizations, which confirm the non-emptiness of the class and provide insights into its structural properties. Furthermore, Fekete\u2013Szeg\u00f6 inequalities are established, enriching the theory of bi-univalent functions. The combination of analytical methods and geometric representations offers a versatile framework for future research in geometric function theory.<\/jats:p>","DOI":"10.3390\/sym17060884","type":"journal-article","created":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T08:34:32Z","timestamp":1749112472000},"page":"884","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Gregory Polynomials Within Sakaguchi-Type Function Classes: Analytical Estimates and Geometric Behavior"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7934-0339","authenticated-orcid":false,"given":"Arzu","family":"Akg\u00fcl","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Science, Kocaeli University, 41001 Kocaeli, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,5]]},"reference":[{"key":"ref_1","unstructured":"Jordan, C. 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