{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T01:07:00Z","timestamp":1776906420459,"version":"3.51.2"},"reference-count":40,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T00:00:00Z","timestamp":1666051200000},"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>In the past few years, many scholars gave much attention to the use of q-calculus in geometric functions theory, and they defined new subclasses of analytic and harmonic functions. While using the symmetric q-calculus in geometric function theory, very little work has been published so far. In this research, with the help of fundamental concepts of symmetric q-calculus and the symmetric q-Salagean differential operator for harmonic functions, we define a new class of harmonic functions connected with Janowski functions SH0\u02dcm,q,A,B. First, we illustrate the necessary and sufficient convolution condition for SH0\u02dcm,q,A,B and then prove that this sufficient condition is a sense preserving and univalent, and it is necessary for its subclass TSH0\u02dcm,q,A,B. Furthermore, by using this necessary and sufficient coefficient condition, we establish some novel results, particularly convexity, compactness, radii of q-starlike and q-convex functions of order \u03b1, and extreme points for this newly defined class of harmonic functions. Our results are the generalizations of some previous known results.<\/jats:p>","DOI":"10.3390\/sym14102188","type":"journal-article","created":{"date-parts":[[2022,10,19]],"date-time":"2022-10-19T02:54:25Z","timestamp":1666148065000},"page":"2188","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Applications of Symmetric Quantum Calculus to the Class of Harmonic Functions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5053-5028","authenticated-orcid":false,"given":"Mohammad Faisal","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5287-4656","authenticated-orcid":false,"given":"Isra","family":"Al-Shbeil","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan"}]},{"given":"Najla","family":"Aloraini","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Arts and Sciences Onaizah, Qassim University, Buraidah 51452, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1123-8578","authenticated-orcid":false,"given":"Nazar","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0361-4887","authenticated-orcid":false,"given":"Shahid","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,18]]},"reference":[{"key":"ref_1","unstructured":"Ponnusamy, S., and Silverman, H. 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